Diszkrét és folytonos: a gráfelmélet, algebra, analízis és geometria találkozási pontjai = Discrete and Continuous: interfaces between graph theory, algebra, analysis and geometry

Sok eredmény született a gráfok növekvő konvergens sorozataival és azok limesz-objektumaival, ill. az ezek vizsgálatára szolgáló gráf-algebrákkal kapcsolatban. Kidolgozásra kerültek a nagyon nagy sűrű gráfok (hálózatok) matematikai elméletének alapjai, és ezek alkalmazásai az extremális gráfelmélet területén. Aktív és eredményes kutatás folyt a diszkrét matematika más, klasszikus matematikai területekkel való kapcsolatával kapcsolatban: topológia (a topológiai módszer alkalmazása gráfok magjára, ill a csomók elmélete), geometriai szerkezetek merevsége (a Molekuláris Sejtés bizonyítása 2 dimenzióban), diszkrét geometriai (Bang sejtésének bizonyítása), véges geometriák (lefogási problémák, extremális problémák q-analogonjai), algebra (félcsoport varietások, gráfhatványok színezése), számelmélet (additív számelmélet, Heilbronn probléma), továbbá gráfalgoritmusok (stabilis párosítások, biológiai alkalmazások)) területén. | 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)

EFFICIENCY AND COST MODELLING OF THERMAL POWER PLANTS

The proper characterization of energy suppliers is one of the most important components in the modelling of the supply/demand relations of the electricity market. Power generation capacity i. e. power plants constitute the supply side of the relation in the electricity market. The supply of power stations develops as the power stations attempt to achieve the greatest profit possible with the given prices and other limitations. The cost of operation and the cost of load increment are thus the most important characteristics of their behaviour on the market. In most electricity market models, however, it is not taken into account that the efficiency of a power station also depends on the level of the load, on the type and age of the power plant, and on environmental considerations. The trade in electricity on the free market cannot rely on models where these essential parameters are omitted. Such an incomplete model could lead to a situation where a particular power station would be run either only at its full capacity or else be entirely deactivated depending on the prices prevailing on the free market. The reality is rather that the marginal cost of power generation might also be described by a function using the efficiency function. The derived marginal cost function gives the supply curve of the power station. The load level dependent efficiency function can be used not only for market modelling, but also for determining the pollutant and CO2 emissions of the power station, as well as shedding light on the conditions for successfully entering the market. Based on the measurement data our paper presents mathematical models that might be used for the determination of the load dependent efficiency functions of coal, oil, or gas fuelled power stations (steam turbine, gas turbine, combined cycle) and IC engine based combined heat and power stations. These efficiency functions could also contribute to modelling market conditions and determining the environmental impact of power stations