We consider a two-echelon single commodity inventory system with one warehouse(supplier) at the higher echelon and one retailer at the lower echelon. The retailer stocks individual items of a commodity and satisfies unit demands which occur according to a Poisson process. The supplier stocks these items in packets and uses these packetsto: (i) satisfy the demands that occur for single packet an...

The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. W...

A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A cast puzzle is a type of disentanglement puzzle, where each piece is a zinc die-casting alloy. In this paper, we consider the generalized cast puzzle problem whose input is the layout of a finite number of pieces (polyhedrons) in the 3-dimension...

A sufficient condition for exact linearization of a nonlinear system via an exponential transformation is obtained as a Lagrange partial differential equation. When its solution can be found, the transformation is determined such that the nonlinear systemis exactly converted into a linear system with arbitrary dynamics. When the transformation is invertible, this technique can be applied to exa...

We define a transformation of models of additivefree propositional linear logic, closely related to de Paiva’s dialectica categories, but with a modified exponential based on Oliva’s dialectica interpretation of higher-order linear logic. As a result of this modification we obtain an elegant factorisation of dialectica models as linear-nonlinear adjunctions. From the point of view of game seman...