Lubell proved this by observing that the left-hand side is a probability: it is simply the probability that a maximal chain, chosen uniformly at random, intersects A. The LYM inequality implies that an antichain in P([n]) has size at most ( n bn/2c ) , the size of the ‘middle layer’ in P([n]). (This can also be proved by partitioning P([n]) into ( n bn/2c ) disjoint chains.) Bollobás’ Inequalit...

In this paper we consider linear, lumped, finite networks composed of interconnections of time-variable and passive resistances, capacitances, inductances, gyrators and transformers. We assume an impedance matrix port description of the network is given and solve the problem of synthesising the impedance, that is, we determine a set of passive elements and a scheme of interconnection which yiel...

This paper presents a method of the determination of a positive stable realisation of the fractional continuous-time positive system consisting of n subsystems with one fractional order and with different fractional orders. For the proposed method, a digraph-based algorithm was constructed. In this paper, we have shown how we can realise the transfer matrix using electrical circuits consisting ...

Abstract—In this paper, we consider the resistances and inductances extraction from finite conducting metals. To remedy the weakness of volume integral equation, we extend the usage of a surface integral equation method from analyzing finite conducting rectangular wire strip to analyzing arbitrarily shaped geometry. Moreover the multilevel Green function method (MLGFIM) with a complexity of O(N...