5 research outputs found
A chronikus pancreatitis differenciál-diagnózisa próbaétkezés hatására bekövetkező serum amylase emelkedése alapján
DiszkrĂ©t Ă©s folytonos: a gráfelmĂ©let, algebra, analĂzis Ă©s geometria találkozási pontjai = Discrete and Continuous: interfaces between graph theory, algebra, analysis and geometry
Sok eredmĂ©ny szĂĽletett a gráfok növekvĹ‘ konvergens sorozataival Ă©s azok limesz-objektumaival, ill. az ezek vizsgálatára szolgálĂł gráf-algebrákkal kapcsolatban. Kidolgozásra kerĂĽltek a nagyon nagy sűrű gráfok (hálĂłzatok) matematikai elmĂ©letĂ©nek alapjai, Ă©s ezek alkalmazásai az extremális gráfelmĂ©let terĂĽletĂ©n. AktĂv Ă©s eredmĂ©nyes kutatás folyt a diszkrĂ©t matematika más, klasszikus matematikai terĂĽletekkel valĂł kapcsolatával kapcsolatban: topolĂłgia (a topolĂłgiai mĂłdszer alkalmazása gráfok magjára, ill a csomĂłk elmĂ©lete), geometriai szerkezetek merevsĂ©ge (a Molekuláris SejtĂ©s bizonyĂtása 2 dimenziĂłban), diszkrĂ©t geometriai (Bang sejtĂ©sĂ©nek bizonyĂtása), vĂ©ges geometriák (lefogási problĂ©mák, extremális problĂ©mák q-analogonjai), algebra (fĂ©lcsoport varietások, gráfhatványok szĂnezĂ©se), számelmĂ©let (additĂv számelmĂ©let, Heilbronn problĂ©ma), továbbá gráfalgoritmusok (stabilis párosĂtások, biolĂłgiai alkalmazások)) terĂĽletĂ©n. | Several results were obtained in connection with convergent growing sequences of graphs and their limit objects, and with graph algebras facilitating their study. Basic concepts for the study of very large dense graphs were worked out, along with their applications to extremal graph theory. Active and successful research was conducted concerning the interaction of discrete mathematics with other, classical areas of mathematics: topology (applications of topology in the study of kernels of graphs, and the theory of knots), rigidity of geometric structures (proof of the Molecular Conjecture in 2 dimensions), discrete geometry (proof of the conjecture of Bang), finite geometries (blocking problems, q-analogues of extremal problems), algebra (semigroup varieties, coloring of graph powers), number theory (additive number theory, heilbronn problem), and graph algorithms (stable matchings, applications in biology)
Pre-excitation studies for rubidium-plasma generation
The key element in the Proton-Driven-Plasma-Wake-Field-Accelerator (AWAKE) project is the generation of highly uniform plasma from Rubidium vapor. The standard way to achieve full ionization is to use high power laser which can assure the over-barrier-ionization (OBI) along the 10 meters long active region. The Wigner-team in Budapest is investigating an alternative way of uniform plasma generation. The proposed Resonance Enhanced Multi Photon Ionization (REMPI) scheme probably can be realized by much less laser power. In the following the resonant pre-excitations of the Rb atoms are investigated, theoretically and the status report about the preparatory work on the experiment are presented