Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Non-uniqueness through duality in the von Neumann growth models

Duality can be viewed as the soul of each von Neumann growth model. This is not at all surprising because von Neumann (1955), a mathematical genius, extensively studied quantum mechanics which involves a “dual nature” (electromagnetic waves and discrete corpuscules or light quanta). This may have had some influence on developing his own economic duality concept. The main object of this paper is to restore the spirit of economic duality in the investigations of the multiple von Neumann equilibria. By means of the (ir)reducibility taxonomy in Móczár (1995) the author transforms the primal canonical decomposition given by Bromek (1974) in the von Neumann growth model into the synergistic primal and dual canonical decomposition. This enables us to obtain all the information about the steadily maintainable states of growth sustained by the compatible price-constellations at each distinct expansion factor.

Detection of self-complementary inverted repeats by single forward primer driven PCR

Inverted repeat gene structures designed for silencing functional genes have been widely used both in academic and applied research. The correct orientations of such structures are usually validated with restriction analysis and/or sequencing. We speculated that the inverted repeat nature of such constructs can be shown by a simple PCR reaction with a single forward primer. To test this hypothesis five different constructs were established from grapevine sequences in a hairpin-intron style silencing system. We were able to amplify the appropriate products in each case. Thus a forward-primed PCR alone may be sufficient to prove the inverted repeat nature of the desired constructs.