Diszkrét és konvex geometria = Discrete and convex geometry

R^3-ben n pont meghataroz legalabb const n^{77/141 -epsilon} tavolsagot (epsilon >0 tetsz.) R^3-ben n nem koplanaris pont (n>6 paratlan) meghataroz legalabb 2n-5 iranyt, es ez minden fenti n-re pontos. Egy racsteglatestnek, amelybe teljes n-es graf belerajzolhato, hogy a csucsok racspontok, es az elek mas csucson nem mennek at, minimalis terfogata const n^{3/2}. R^3-ben C^2 konvex testeknek korlatozott elszamu konvex poliederekkel torteno terfogatapproximaciojat visgaltuk, es erre aszimptotikus formulat adtunk. Minden harmadfoku graf egyenes elekkel sikba rajzolhato ugy hogy el nem tartalmaz mas csucsot, es az elek iranyai szama legfeljebb const. Az egysegkor veges sok konvex tartomanyra bontasa eseten ezek beirt korei sugarai osszege legalabb 1. R^n-ben egy 2 atlagszelessegu konvex test kore irt szimplex atlagszelessege legalabb akkora mint az egyseggomb kore irt szabalyos szimplexe. R^n-ben (n>1) ket konvex test, amelyek barmely kongruens peldanyainak metszete/uniojuk konvex burka centralszimmetrikus, kongruens gombok. Minden veges sikbeli ponthalmazban van Hamilton-ut, hogy egyik szog sem kisebb 20 foknal. R^n-ben 0-ra csillagszeru testet meghataroznak a linearis (n-1)-alterekkel valo metszetei teruletei es sulypontjai. Fix k-ra n pontu, gorbevonalakkal sikbarajzolt grafokra, amelyeknel nincs k paronkent metszo el, az elszamra a korabbiaknal sokkal jobb felso becslest adtunk. | In R^3 n points determine at least const n^{77/141-epsilon} distances (epsilon >0 arbitrary). In R^3 n not coplanar points (n>6 odd) determine at least 2n-5 directions, sharp for each above n. In R^3 lattice rectangular box, in which complete graph on n vertices can be drawn, vertices being lattice points, edges not containing other vertices, has minimal volume const n^{3/2}. In R^3 we investigated volume approximation of C^2 convex bodies by convex polyhedra with number of edges bounded above, gave asymptotic formula. Each 3rd degree graph can be drawn in R^2 with straight edges, no edge containing other vertices, number of directions of edges bounded. Decomposing the unit disc to finitely many convex domains, sum of the inradii is >= 1. In R^n average width of simplex, circumscribed to convex body of constant width 2, is >= that of regular simplex circumscribed to unit ball. In R^n (n>1) two convex bodies, intersection/convex hull of union of any congruent copies of which being centrally symmetric, are congruent balls. Finite set in R^2 has Hamilton line, each angle >= 20 degrees. In R^n body starlike w.r.t. 0 is determined by areas and barycentres of its sections with linear (n-1)-subspaces. We gave, for fixed k, for edge numbers of graphs with n vertices, drawn in R^2 with curvilinear edges, having no k pairwise intersecting edges, estimates from above, much better than earlier ones

Late Miocene sedimentary record of the Danube / Kisalföld Basin: interregional correlation of depositional systems, stratigraphy and structural evolution

The Danube / Kisalföld Basin is the north-western sub-basin of the Pannonian Basin System. The lithostratigraphic subdivision of the several-km-thick Upper Miocene to Pliocene sedimentary succession related to Lake Pannon has been developed independently in Slovakia and Hungary. A study of the sedimentary formations across the entire basin led us to claim that these formations are identical or similar between the two basin parts to such an extent that their correlation is indeed a matter of nomenclature only. Nemčiňany corresponds to the Kálla Formation, representing locally derived coarse clastics along the basin margins (11– 9.5 Ma). The deep lacustrine sediments are collectively designated the Ivanka Formation in Slovakia, while in Hungary they are subdivided into Szák (fine-grained transgressive deposits above basement highs, 10.5 – 8.9 Ma), Endrőd (deep lacustrine marls, 11.6 –10 Ma), Szolnok (turbidites, 10.5 – 9.2 Ma) and Algyő Formations (fine-grained slope deposits, 10 – 9 Ma). The Beladice Formation represents shallow lacustrine deltaic deposits, fully corresponding to Újfalu (10.5 – 8.7 Ma). The overlying fluvial deposits are the Volkovce and Zagyva Formations (10 – 6 Ma). The synoptic description and characterization of these sediments offer a basin-wide insight into the development of the basin during the Late Miocene. The turbidite systems, the slope, the overlying deltaic and fluvial systems are all genetically related and are coeval at any time slice after the regression of Lake Pannon initiated about 10 Ma ago. All these formations get younger towards the S, SE as the progradation of the shelf-slope went on. The basin got filled up to lake level by 8.7 Ma, since then fluvial deposition dominated

Late Miocene sedimentary record of the Danube/Kisalföld Basin: interregional correlation of depositional systems, stratigraphy and structural evolution

The Danube / Kisalföld Basin is the north-western sub-basin of the Pannonian Basin System. The lithostratigraphic subdivision of the several-km-thick Upper Miocene to Pliocene sedimentary succession related to Lake Pannon has been developed independently in Slovakia and Hungary. A study of the sedimentary formations across the entire basin led us to claim that these formations are identical or similar between the two basin parts to such an extent that their correlation is indeed a matter of nomenclature only. Nemčiňany corresponds to the Kálla Formation, representing locally derived coarse clastics along the basin margins (11- 9.5 Ma). The deep lacustrine sediments are collectively designated the Ivanka Formation in Slovakia, while in Hungary they are subdivided into Szák (fine-grained transgressive deposits above basement highs, 10.5 - 8.9 Ma), Endrőd (deep lacustrine marls, 11.6 -10 Ma), Szolnok (turbidites, 10.5 - 9.2 Ma) and Algyő Formations (fine-grained slope deposits, 10 - 9 Ma). The Beladice Formation represents shallow lacustrine deltaic deposits, fully corresponding to Újfalu (10.5 - 8.7 Ma). The overlying fluvial deposits are the Volkovce and Zagyva Formations (10 - 6 Ma). The synoptic description and characterization of these sediments offer a basin-wide insight into the development of the basin during the Late Miocene. The turbidite systems, the slope, the overlying deltaic and fluvial systems are all genetically related and are coeval at any time slice after the regression of Lake Pannon initiated about 10 Ma ago. All these formations get younger towards the S, SE as the progradation of the shelf-slope went on. The basin got filled up to lake level by 8.7 Ma, since then fluvial deposition dominated