The structure constants cλμ determine the classical Schubert calculus on G(m,n). It has been known for some time that the integers cλμ in formulas (1) and (2) coincide. Following the work of Giambelli [G1] [G2], this is proved formally by relating both products to the multiplication of Schur S-polynomials; a precise argument along these lines was given by Lesieur [Les]. It is natural to ask for...

ing from these examples, a calculus in our framework consists of a collection of types, typed programs, typed contexts, a notion of observation and a notion of closedness. In the following we use a slightly more neutral terminology and, instead ACM Transactions on Programming Languages and Systems, Vol. V, No. N, Month 20YY. Correctness of Program Translations for Observational Semantics · 9 of...

Non-determined game logic is the logic of two player board games where the game may end in a draw: unlike the case with determined games, a loss of one player does not necessarily constitute of a win of the other player. A calculus for non-determined game logic is given in [4] and shown to be complete. The calculus adds a new rule for the treatment of greatest fixpoints, and a new unfolding axi...

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we believe is conducive to automation. 1 A Semantic Calculus for Intuitionistic Kripke Models In Rothenberg (2010), we use correspondence theory (Blackburn et al....

1. INTRODUCTION. A common theme in all of mathematics is deciding when two seemingly different objects are actually the same in some sense. For example, every elementary school student knows that, despite outward appearances, the fractions 2/3 and 10/15 are the same. The calculus student knows that the functions f (x) = 3x and g(x) = (3x

This paper aims at investigating the superiority of power allocation strategies, based on calculus of variations in a point-to-point two-way relay-assisted channel incorporating the amplify and forward strategy. Single and multilayer coding strategies for two cases of having and not having the channel state information (CSI) at the transmitters are studied, respectively. Using the notion of cal...