253 research outputs found
A fejszámoló Bolyai Farkas: Farkas Bolyai as a Mental Calculator / Farkas Bolyai și calculul mintal
Get PDFIn 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
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)
Get PDFAbstract
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
Stability conditions for the non-linear McKendrick equations
Get PDFNon-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
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
Fridericia miraflores Sesma and Dozsa-Farkas 1993
No full textFridericia miraflores Sesma and Dózsa-Farkas, 1993 Fridericia miraflores Sesma and Dózsa-Farkas, 1993, pp. 252–254, figures 8–14. Fridericia miraflores, Rota 1995, pp. 211–212, tables 5–6; Rota and Healy 1999, p. 58; Rota et al. 2013, table 1 and figure 3 (species ‘s25’); Rota et al. 2014, tables 1, 2 and Suppl. 1. Fridericia sylvatica, Schmelz 2003, pp. 330–333, figure 65A–H; Schmelz and Collado 2010, pp. 130, 142. Material examined Published material. Specimens from Tuscany, Latium and Calabria (Rota 1995). New material (in the author’ s collection). 12 specimens from Italy, Campania (Ca-1), 14.05.2009 and 27.10.2009. 32 specimens from Campania (Ca-2), plots N2 and N3, 13.05.2009 and 26.10.2009. Remarks This is one of few species in Fridericia having the clitellum interrupted both dorsally and ventrally (Rota and Healy 1999, p. 58; see also Schmelz 2003, as F. sylvatica). This feature and the occurrence of ventral pharyngeal glands in VII (Schmelz 2003, as F. sylvatica) is confirmed for the present and previous material from Italy (as well as for specimens from Algeria), including those with short diverticula. The synonymy of this species with the poorly defined F. sylvatica Healy, 1979 was established by Schmelz (2003), on the basis of the similar chaetal formula and the laterally projecting spermathecal diverticula, and despite important differences in the two original descriptions (size of chaetae, origin of the dorsal vessel, variation in size of the spermathecal gland) and the lack of type material of F. sylvatica. Schmelz (2003) himself discovered that the sole specimen (submature and incomplete) labelled as type of F. sylvatica was not compatible with any of the key characters in the original diagnosis. Although F. miraflores can be collected at the type locality of F. sylvatica (UCD campus, Dublin) (Rota 1995), I believe the circumstances rather suggest that F. sylvatica should be considered a nomen dubium, in that (1) ‘the taxonomic identity of the taxon cannot be determined from its existing name-bearing type’ (ICZN 1999: Art. 75.6), and (2) the original description of F. sylvatica probably involved one or more different species (in particular, the reported variation in the spermatheca towards more globular ampullar diverticula and larger ectal gland point to F. globuligera Rota, 1995, a species also present in the UCD area; own unpublished record). In conclusion, the originally better described and type-based F. miraflores is to be regarded as a valid name. This choice is consistent with the reasoning by Schmelz (2003) on the analogous cases involving F. tirolensis Schmidegg, 1938 and F. discifera Healy, 1975. Distribution Euro-Mediterranean. Present in both seasons at Naples sites. Funding This research was partly supported by a grant from MIUR (PRIN-2007AH8KT8, coordinator Professor Anna Alfani, University of Salerno).Published as part of Rota, Emilia, 2015, Five new species of Enchytraeidae (Annelida: Clitellata) from Mediterranean woodlands of Italy and reaffirmed validity of Achaeta etrusca, Fridericia bulbosa and F. miraflores, pp. 1987-2020 in Journal of Natural History 49 (33) on pages 2017-2018, DOI: 10.1080/00222933.2015.1009514, http://zenodo.org/record/399798
A -fi végű magyar családnevek típusai és története
Get PDFThe types and history of Hungarian surnames ending in -fi (‘son of’)
This paper presents the types, the history and some related problems of surnames including the element -fi (‘son of’), originally a posterior constituent of compounds, which developed into a derivative suffix producing surnames in Hungarian. This surname type has not been discussed frequently in the literature, so its comprehensive survey, which reconsiders earlier remarks as well, is justifiable. The author examines the role of the relevant family names among the Hungarian historical surnames that have evolved naturally; among the artificial surnames formed in the 19th–20th centuries in the process of official name changes; and among contemporary surnames. Characteristics and relations of these different layers of the Hungarian surname stock are explored by analysing statistics based on some large corpora of representative value. The author also searches for explanations behind the observed differences. The paper examines the origins, the development and the possible changes of this name type, identifying many influential background features in language, name and cultural history. The author presents the occurrence and the frequency of the name type and its important representatives, taking name geographical, temporal and social factors into consideration. Relations to other name types as well as to surnames seemingly ending in -fi are also treated. By elaborating a comprehensive approach to this type of surname structure, the author wishes to point out the importance and efficiency of the separate and joint examinations of the different layers of the surname stock
The strong maximal rank conjecture and moduli spaces of curves
Get PDFBuilding on recent work of the authors, we use degenerations to chains of elliptic curves to prove two cases of the Aprodu-Farkas strong maximal rank conjecture, in genus and . This constitutes a major step forward in Farkas\u27 program to prove that the moduli spaces of curves of genus and are of general type. Our techniques involve a combination of the Eisenbud-Harris theory of limit linear series, and the notion of linked linear series developed by the second author.59 pages. v3: Farkas has informed us that his divisor class computation does not suffice to reduce the moduli spaces being of general type to the corresponding cases of the strong maximal rank conjecture: a second type of excess degeneracy also has to be ruled out. We have accordingly removed the implications on the moduli spaces pending further study of the second form of degenerac
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