415 research outputs found
A fejszámoló Bolyai Farkas: Farkas Bolyai as a Mental Calculator / Farkas Bolyai și calculul mintal
No full textIn his childhood, the Hungarian mathematician, Farkas Bolyai (1775–1856) was a very good mental calculator. He calculated the square and cube roots of 14-digit numbers without pen and paper. In his legacy we found an interesting, but a little bit mysterious manuscript on the cube roots. Fortunately, we understood this paper based on a Hungarian arithmetical book by Lőrincz Koretz (1805–1871). The author of this book was a piarist teacher in Hungary. This paper shows some examples based on the unknown József Farczádi Nagy’s calculations of the cube roots.
Rezumat
În copilărie, matematicianul maghiar Farkas Bolyai (1775–1856) a fost capabil să extragă rădăcini pătrate și cubice din numere de 14 cifre. În moștenirea sa am găsit un manuscris interesant, deși puțin misterios, despre extragerea cubică. Din fericire, descifrarea conținutului s-a reușit pe baza unei cărți de matematică a lui Lőrinc Koretz (1805–1871). Autorul acestui volum a fost un profesor piarist. Prezentul articol dicută câteva exemple bazate pe calculele necunoscute ale lui József Farczádi Nagy ale rădăcinilor cubului.
Kivonat
Bolyai Farkas (1775–1856) már gyermekkorában 14 jegyű számból is tudott fejben négyzet- és köbgyököt vonni. Hagyatékában egy érdekes, bár egy kicsit titokzatos kéziratot találtunk, amely a köbgyökvonásról szól. Szerencsére sikerült megfejtetni a tartalmát Koretz Lőrincz (1805–1871) egy számtankönyve alapján. E kötet szerzője kegyesrendi tanár volt. Dolgozatunk néhány példát mutat be Farczádi Nagy József köbgyökvonási módszeréről
Primal and Dual Characterizations for Farkas Type Lemmas in Terms of Closedness Criteria
No full textThis paper deals with the characterization, in terms of closedness of certain sets regarding other sets, of Farkas lemmas determining when the upperlevel set of a convex function f contains a set of the form C ∩ −1 (D), where C and D are convex sets (not necessarily cones) in locally convex spaces X (with topological dual X′) and Y, respectively, while is a continuous linear operator from X to Y. More in detail, each of the mentioned characterizations of Farkas type lemmas consists in the closedness of certain subset of either one of the “primal” spaces X × Y × ℝ and Y × ℝ, or of the “dual” space X′ × ℝ, regarding some singleton set of the corresponding space. Moreover, the paper also provides an existence theorem for the feasible set C ∩ −1 (D) in terms of the closedness of certain subset of the dual space X′ ×ℝ regarding the singleton set formed by the null element. These results are illustrated with significant applications to constrained convex minimization problems and to functional approximation by polynomials.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The research of the first author has been partly supported by the project “Generalized Farkas lemma for a family of adjustable systems with uncertainty and applications”, Vietnam National University-Ho Chi Minh city, Vietnam. The research of the second author has been supported by Grant PID2022-136399NB-C21, funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU
Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation
No full textPrecipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool to investigate the statistical interdependence of many interacting elements, is used here to analyze the spatial dynamics of annual precipitation over seventy years (1941-2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only. Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns
Farkas-type theorems for positively homogeneous semi-infinite systems
No full textThis article deals with systems of infinitely many inequalities involving functions that are positively homogeneous over a nonempty convex cone of the Euclidean space. Generalized convex conjugation theory is applied to derive a Farkas-type and a Gale-type theorem for this kind of systems. These results are particularized for linear and min-type inequality systems.The research of the first author has been partially supported by the Spanish Ministry of Science and Technology, project BFM2002-04114-C02, and by the sabbatical program of Alicante University. The work of the second author has been supported by the Spanish Ministry of Science and Technology, project BEC2002-00642, and by the Departament d’Universitats, Recerca i Societat de la Informació, Direcció General de Recerca de la Generalitat de Catalunya, project 2001SGR-00162. He also thanks the support of the Barcelona Economics Program of CREA
Foliicolous lichen collections on Mount Kanga, Tanzania (East Africa)
No full textAbstract
The Tanzanian Mt Kanga was at first visited by Tamás Pócs in 1987 when he collected foliicolous lichens in lowland rainforest between 800 and 900 m elevation and in submontane rainforest between 900 and 1,250 m. Later, in 1989 he returned there with participants of the Nguru Mts expedition, when the author collected further lichens including foliicolous ones in three different forest types (dry evergreen and semi-evergreen forest at 600–800 m, submontane rainforest at 850–1,200 m and rocky forest at 1,200–1,300 m). Altogether 37 species became known from the area. The comparison of collections revealed that submontane rainforests (including rocky forests) are the richest of the studied forest types in foliicolous lichens. Mt Kanga is characterised by rare species like Calopadia editae discovered by Antonín Vězda in material from Mt Kanga, described and validated in 2011 by Chaves and Lücking based on materials from Mt Kanga and Costa Rica. The new combination Brasilicia dimerelloides (Vězda) Farkas is introduced. The palaeotropical Fouragea viridistellata (Sérus., Lücking et Sparrius) Ertz et Frisch described in 2008 is reported here as new for Tanzania
Modelling Driver Interdependent Behaviour in Agent-Based Traffic Simulations for Disaster Management
No full textAccurate modelling of driver behaviour in evacuations is vitally important in creating realistic training environments for disaster management. However, few current models have satisfactorily incorporated the variety of factors that affect driver behaviour. In particular, the interdependence of driver behaviours is often seen in real-world evacuations, but is not represented in current state-of-the art traffic simulators. To address this shortcoming, we present an agent-based behaviour model based on the social forces model of crowds. Our model uses utility-based path trees to represent the forces which affect a driver's decisions. We demonstrate, by using a metric of route similarity, that our model is able to reproduce the real-life evacuation behaviour whereby drivers follow the routes taken by others. The model is compared to the two most commonly used route choice algorithms, that of quickest route and real-time re-routing, on three road networks: an artificial "ladder" network, and those of Lousiana, USA and Southampton, UK. When our route choice forces model is used our measure of route similarity increases by 21%-93%. Furthermore, a qualitative comparison demonstrates that the model can reproduce patterns of behaviour observed in the 2005 evacuation of the New Orleans area during Hurricane Katrina
Stability conditions for the non-linear McKendrick equations
No full textNon-linear McKendrick equation with age-dependent mortality and fertility is considered. The author [Appl. Math. Comput. 131 (1) (2002) 107] deduced the characteristic equation whose roots determine the stability. We are able to give sufficient conditions for the stability of the stationary solutions of the system in some cases
New Quercus-feeding Brevulacus species, redescription of Rhyncaphytoptus cerrifoliae Farkas and new Eriophyoid mite records from Hungary (Acari: Prostigmata: Eriophyoidea)
No full textAuthor made regular mite collectings between 1990 and 2010 on ornamental trees and shrubs, on streets, parks, in city greenery, forests, botanical gardens and private gardens, in various localities of Hungary. During this survey a new Quercus-infesting eriophyoid mite species was collected: Brevulacus carpathicus n. sp. is described and illustrated from Quercus petraea. Rhyncaphytoptus cerrifoliae Farkas is redescribed from Quercus cerris. Both species produce wax and are vagrant on the leaf undersurface. Two other species, viz. Aceria cichorii Petanović, Boczek et Shi and Cecidophyes tristernalis (Nalepa) are new species for the fauna of Hungary. Some faunistic data on the known taxa from this country are included
Additional file 4: of Phylogenetic analysis of Spirocerca lupi and Spirocerca vulpis reveal high genetic diversity and intra-individual variation
No full textFigure S3. Principal coordinate analysis (PCoA) scatter plot showing Neiâs genetic distances of the ITS1 sequences of S. lupi (a) and Spirocerca spp. (b) according to the sampling locations. The percentage of total variation attributed to each axis is indicated next to each coordinate. Each specimen is represented as a color-coded circle according to the geographical origin. (TIF 385 kb
Lukács in Self-Translation: The Necessity of Contingency in <i>The Soul and the Forms</i>
No full text A series of meditations on history and criticism, György Lukács's The Soul and the Forms appeared first in Hungarian in 1910 and then in German in 1911—arguably having been translated by the author himself, as a work of mourning. Despite renewed interest in the work, English-language editions have been taken from the German translation and barely consider the Hungarian version. This essay argues that an exemplary skirmish takes place in translation between the Hungarian and the German texts, as Lukács shifts from an Epicurean-Lucretian to a Stoicist view of causality. Not unlike in the early notebooks of Marx, a materialist Lukács can be located in his first collection of essays, despite the fact that it is usually pigeonholed as part of his grand idealist phase. Farkas is particularly interested in how Lukács's self-translation washes over a Romantic concept of irony as Lukács posits the necessity of a mixture of necessity and contingency as the origin of the critic's irony, a move that undermines his own non-totalizing view of irony as a structural principle of the novel in his 1917 work The Theory of the Novel. </jats:p
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