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Starting with the typology of action as conceived by Max Weber the explication of the terms introduced by him shows that these concepts are by far too crude and that he omitted several important types of action. On the one side, affective behaviour and emotional action have to be differentiated since the latter is by no means irrational. Fritz Heider for example spoke of a "logic of emotions" decades ago. On the other side, rationality in the sense of "Zweckrationalität" has to be conceived as a from of addictive behaviour. It is true, as Gary S. Becker has shown, That we can speak of rational addiction", but it is clear that if person  becomes totally dependent on a drug or an ideological goal, his behaviour becomes selfdestructive and this can hardly be named "rational". A third serious problem of Weber's typology of action is that he never made quite clear what a "value rational" ertrational) action means. On the basis of the so called "pattern variables", defined by Talcott Parsons, and this theory os socialisations an attempt is made in this article to delver an explication of the term of "Wertrationalität" (value-rationality). On the basis of the 5 pattern variables, each being conceived as consisting of five dichomoties, 32 possible action orientations are dervied, and some of these can be identified as different types of rationality. If we conceive "Wertrationalität" and Zweckrationalität" on this basis, we find that "value rationality" always implies a more complicated calculation than "Zweckrationalität". Furthermore, it implies often enough, that not all the means should be used , even if a person could dispose of them. Seen on the short run, "value-rational" orientation therefore implies a  handicap if a person has to compete with a "zweckrational" actor. Therefore one schould expect an evolutionary process by wich "value-rational" actors are omitted from the social system as "loosers". A detalied analysis shows, however, that persons with a universalistic value  orientation have a superior chance to from common value systems with those who are also universalistically oriented, if they act in a value-rational way, and that they therefore have superior chances in the competition with "zweckrational" actors on the long run. A second very serious disadvantage of "zweckrational" actors was detected already by Max Weber himself: "Zweckrationalität" itself becomes  in its purest form an addiction. Success is sought in this case only because it is successful. If success is the ultimate goal of "zweckrational" orientation for its own sake (as a thrill), action becomes totally irrational. This will be the consequence, because  no material goals exist anymore, and the ultimate goal of action gets a formal character. Therefore the final result of "zweckrational" action is a basically nihilistic orientation.

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Abstract  

We prove that the “quadratic irrational rotation” exhibits a central limit theorem. More precisely, let α be an arbitrary real root of a quadratic equation with integer coefficients; say, α =

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sqrt 2$$ \end{document}
. Given any rational number 0 < x < 1 (say, x = 1/2) and any positive integer n, we count the number of elements of the sequence α, 2α, 3α, …, modulo 1 that fall into the subinterval [0, x]. We prove that this counting number satisfies a central limit theorem in the following sense. First, we subtract the “expected number” nx from the counting number, and study the typical fluctuation of this difference as n runs in a long interval 1 ≤ nN. Depending on α and x, we may need an extra additive correction of constant times logarithm of N; furthermore, what we always need is a multiplicative correction: division by (another) constant times square root of logarithm of N. If N is large, the distribution of this renormalized counting number, as n runs in 1 ≤ nN, is very close to the standard normal distribution (bell shaped curve), and the corresponding error term tends to zero as N tends to infinity. This is the main result of the paper (see Theorem 1.1). The proof is rather complicated and long; it has many interesting detours and byproducts. For example, the exact determination of the key constant factors (in the additive and multiplicative norming), which depend on α and x, requires surprisingly deep algebraic tools such as Dedeking sums, the class number of quadratic fields, and generalized class number formulas. The crucial property of a quadratic irrational is the periodicity of its continued fraction. Periodicity means self-similarity, which leads us to Markov chains: our basic probabilistic tool to prove the central limit theorem. We also use a lot of Fourier analysis. Finally, I just mention one byproduct of this research: we solve an old problem of Hardy and Littlewood on diophantine sums. The whole paper consists of an introduction and 17 sections. Part 1 contains the Introduction and Sections 1–7.

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Res ardua vetustis novitatem dare

A leo generosus és idősebb Plinius zoológiája

Antik Tanulmányok
Author: Ágnes Darab

A tanulmány egyetlen szöveg elemzéséből indul ki: idősebb Plinius Naturalis historiájának leírásából az oroszlánról (8, 41–58). Az elemzés ezt a 17 fejezetnyi narratív egységet elhelyezi az enciklopédia zoológiai tárgyú könyveinek, majd a 8. könyvnek a struktúrájában, megállapítja és értelmezi a leírás narratív sajátosságait. Mindezt tágabb összefüggésbe helyezve összeveti a téma legfontosabb előzményével, Aristotelés leírásaival az oroszlánról, illetve kitekint a legfontosabb recepciójára, Ailianos oroszlán-narratíváira. Az irodalmi kontextus mellett fontos szempont a filozófiai háttér: az ember és a természet többi élőlényének viszonyáról kialakított, alapvetően a sztoikus filozófiában gyökerező, a racionalitás-irracionalitás oppozíciójára épített álláspont. Mindennek ismeretében történik meg Plinius oroszlán-narratívájának, valamint az elemzésbe bevont analógiák alapján zoológiájának elhelyezése az antik zoológiai irodalom palettáján.

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“Every Russian writer owes something to Gogol.” This Nabokovian statement questions beliefs traditionally formulated in respect to Gogol’s oeuvre. His book paradoxically introduced by the depiction of the writer’s death implies that the motif of death has a specific impact on the genesis of the artefact. The similar postmodernist theory by Terc echoes in part ideas found in the symbolist perception of Gogol (Annensky, Blok, Rozanov, Merezhkovsky, and Andrei Bely). Gogol’s poetics centred upon this principle, reminiscent of Dante’s Divine Comedy, can be traced throughout the works of Russian authors – a thesis to be scrutinised in a series of forthcoming articles. The irrational in Gogol’s views concerning true art thus shall discard the labels of critical realism and art envisaged as the device meant to perfect human society, consequently via the transmutation of the self shall true art fulfil its ultimate mission. Introducing the dichotomy of ‘poet’ – ‘non-poet’ indicates a precursor of the Solovyovian doctrine of the superman. The ideal of transgression is expressed through applying the medieval interpretation of the language distinguishing Dante’s work, offering a profound reading of texts. The poetics of death penetrating Gogol’s works implicates handling and interpreting of various phenomena of culture synthesised, including models of self-perfection realised by alchemy, freemasonry, and Russian sophiology.

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In the recent years, it has been noted that microorganisms with acquired resistance to almost all available potent antibiotics are increasing worldwide. Hence, the use of antibiotics in every clinical setup has to be organized to avoid irrational use of antibiotics. This study was aimed to establish the pattern of antibiotic sensitivity and relevance of antimicrobial resistance in aerobic Gram-negative bacilli. A total of 103 aerobic Gram-negative bacteria namely Escherichia coli, Klebsiella pne u moniae, E nterobacter spp., Citrobacter koserii, Proteus spp., and Pseudomonas aeruginosa were collected from tertiary care centers around Chennai. Kirby–Bauer Disk Diffusion test and study for genes of cephalosporin, carbapenem, and aminoglycoside resistance were done. A descriptive analysis of the data on altogether 103 clinical urine isolates was performed. All strains showed susceptibility to colistin. The frequency of genes encoding 16S rRNA methylases armA and rmtB were 7.8% and 6.8%, respectively. Among metallo-β-lactamases, bla VIM, bla IMP, and bla NDM-1 were detected in 6.8%, 3.8%, and 3.8%, respectively. One E. coli strain harbored bla SIM-1 gene. Cumulative analysis of data suggested that 30% of the strains carried more than one resistance gene. The current research evidenced the increasing frequency of resistance mechanisms in India. Combined approach of antibiotic restriction, effective surveillance, and good infection control practices are essential to overcome antibiotic resistance.

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Abstract  

We prove that the “quadratic irrational rotation” exhibits a central limit theorem. More precisely, let α be an arbitrary real root of a quadratic equation with integer coefficients; say, . Given any rational number 0 < x < 1 (say, x = 1/2) and any positive integer n, we count the number of elements of the sequence α, 2α, 3α, ..., modulo 1 that fall into the subinterval [0, x]. We prove that this counting number satisfies a central limit theorem in the following sense. First, we subtract the “expected number” nx from the counting number, and study the typical fluctuation of this difference as n runs in a long interval 1 ≤ nN. Depending on α and x, we may need an extra additive correction of constant times logarithm of N; furthermore, what we always need is a multiplicative correction: division by (another) constant times square root of logarithm of N. If N is large, the distribution of this renormalized counting number, as n runs in 1 ≤ nN, is very close to the standard normal distribution (bell shaped curve), and the corresponding error term tends to zero as N tends to infinity. This is the main result of the paper (see Theorem 1.1).

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Journal of Evolutionary Psychology
Authors: Ryo Oda, Kai Hiraishi, Yasuyuki Fukukawa, and Akiko Matsumoto-Oda

Abstract

Possible effects of external and internal factors affecting prosociality in Japanese undergraduates were investigated. We employed social support as an external factor and helping norms, self-consciousness, other-consciousness, self-esteem, and religious attitude as internal factors. Prosociality toward friends/acquaintances was significantly positively correlated with social support from siblings, social support from friends/acquaintances, self-sacrifice norms, and private self-consciousness, whereas prosociality toward strangers was significantly positively correlated with social support from mothers, private self-consciousness, and self-esteem but negatively correlated with social support from siblings. The results support claims of an altruism niche that rest on the assumption that prosociality can be maintained only in an environment or a society in which altruistic acts are rewarded. Among the internal factors, private self-consciousness was the only factor found to correlate with both aspects of prosociality. Higher scores on private selfconsciousness were related to irrational altruism, making people less susceptible to the features of particular situations and, consequently, producing reputational benefits.

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Abstract

The frescoes decorating the stateroom of the Episcopal palace of Szombathely were painted by Franz Anton Maulbertsch in 1783 on commission from bishop János Szily. The lateral walls received scenes from the history of the Roman predecessor of the town Savaria in the form of grisaille murals imitating bronze reliefs. The four paintings – Tiberius Claudius founds Savaria, Septimius Severus is elected emperor, Triumph of Constantinus Chlorus, and Attila chases the Romans out of Pannonia – conjure up the Roman world with a multitude of detail and with historical authenticity. Besides, they also deliberately apply the iconographic and compositional rules of relief sculpture in the Imperial Period. This historicizing rendering is an indicator of the new accent on historism, suggesting the 18th century transformation of the concept of history fed by the recognition of the historical distance between the event and the observer.

The ceiling shows the process of salvation under the governance of Providence. Some elements were borrowed by Maulbertsch from his earlier work in the former library of the Premonstratensian monastery in Louka, Moravia. The theme is the temporal process of the enlightenment of mankind, but the historical examples are replaced here by abstract notions, the time and space coordinates appearing highly generalized. In the middle the allegorical figure of Divine Providence arrives on clouds, with personifications of the Old and New Testaments beneath him suggesting periods in the history of salvation. As a counterpoint to Providence bringing the glimmer of dawn, the Allegory of the Night is depicted at the other end of the ceiling. The two sleeping figures are captives of the lulling power of the fauns symbolizing irrational existence governed by instincts. The pseudo-reliefs and sculptures painted in the corners represent heathenism, the ante legem period of the process of salvation. The medallions show typical episodes of bacchanals of putti, and the grisaille figures most likely repeat motifs of the bacchanal scene in the Louka fresco. The themes of the other three colour frescoes are Europe's apotheosis among the continents, Revelation of the True Religion, and the Apotheosis of Truth in the company of Religion, Humility and the Christian martyrs. It is actually a modernized psychomachy, presenting the victory of Christianity, faith and the virtues over paganism, the instincts and vices. The allegoric groups are witty renderings of conventional formulae.

The rich painted architecture of the ceiling is based on Paul Decker's pattern sheet complemented with neoclassical elements but preserving its irrational character. The illusory architecture, the rivaling lifelikeness of colourful and monochrome figures creates a play of degrees of reality that mobilize the imagination. Maulbertsch's pictorial world can be characterized with the concepts of delicieux and charmant used to describe Mozart's music; his tools of expression convey an ease and serenity that are not light-minded but with the tools of subtle irony and humour invite the viewer for more sophisticated reflections, contrary to the propagandistic allegories.

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Let E 2(V;X; δ) and E 4(V;X; δ) respectively denote the number of vV, vx such that the inequality \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\left| {\lambda _1 p_1 + \lambda _2 p_2 ^2 - v} \right| < v^{ - \delta } $ \end{document} has no solution in primes p 1, p 2, and the number of vV, vx such that the inequality \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\left| {\lambda _1 p_1 ^2 + \lambda _2 p_2 ^2 + \lambda _3 p_3 ^2 + \lambda _4 p_4 ^2 - v} \right| < v^{ - \delta } $ \end{document} has no solution in primes p 1, p 2, p 3, p 4. In both cases, we assume that all λ j are non-zero real numbers satisfying that λ 1/λ 2 is irrational and algebraic, and V is a well-spaced set. In this note we prove that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\begin{gathered} E_2 (\mathcal{V},X,\delta ) \ll X^{\tfrac{7}{8} + 2\delta + \varepsilon } , \hfill \\ E_4 (\mathcal{V},X,\delta ) \ll X^{\tfrac{3}{4} + 4\delta + \varepsilon } . \hfill \\ \end{gathered} $ \end{document}.

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Summary  

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S(x,\alpha\mid X_p):=\sum_{\substack{p_1p_2<x\\ p_1<p_2}} X_{p_1}X_{p_2}e^{2\pi i\alpha p_1p_2},\qquad \pi_2(x)=\sum_{\substack{p_1p_2<x\\ p_1<p_2}} 1,$ \end{document}$ where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $p$ \end{document}, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $p_1$ \end{document}, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $p_2$ \end{document} run over the prime numbers. It is proved that

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\max_{\substack{|X_p|\le 1\\ p}} \frac{{S(x,\alpha,X_p)}}{{\pi_2(x)}} =\Delta(x,\alpha)\to 0\qquad(x\to\infty)$$ \end{document}
for almost all irrational \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\alpha$ \end{document}.

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