We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at the basic definitions and present details of an implementation in the functional programming language Standard ML. This provides a functional approach to gra...

In this paper, we develop an energy method to study finite speed of propagation and waiting time phenomena for the stochastic porous-media equation with linear multiplicative noise in up to three spatial dimensions. Based on a novel iteration technique and on stochastic counterparts of weighted integral estimates used in the deterministic setting, we formulate a sufficient criterion on the grow...

We show that a multiplicative form of Dirichlet’s theorem on simultaneous Diophantine approximation as formulated by Minkowski, cannot be improved for almost all points on any analytic curve on R which is not contained in a proper affine subspace. Such an investigation was initiated by Davenport and Schmidt in the late sixties. The Diophantine problem is then settled via showing that certain se...

in this paper, we use the denition of fuzzy normed spaces givenby bag and samanta and the behaviors of solutions of the additive functionalequation are described. the hyers-ulam stability problem of this equationis discussed and theorems concerning the hyers-ulam-rassias stability of theequation are proved on fuzzy normed linear space.

We analyze variations of multiplicative updates for learning linear functions online. These can be described as substituting exponentiation in the Exponentiated Gradient (EG) algorithm with quadratic and linear functions. Both kinds of updates substitute exponentiation with simpler operations and reduce dependence on the parameter that specifies the sum of the weights during learning. In partic...