Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as non-negative integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called vir...

This paper proposes a new challenging optimization problem, called COOLING-AWARE WORKLOAD PLACEMENT PROBLEM, that looks for a workload placement that optimizes the overall data center power consumption given by the sum of the server power consumption and of the computer room air conditioner power consumption. We formulate CWPP as a Mixed Integer Non Linear Problem using a cross-interference mat...

We prove a representation theorem of projections of sets of integer points by an integer matrix W . Our result can be seen as a polyhedral analogue of several classical and recent results related to the Frobenius problem. Our result is motivated by a large class of non-linear integer optimization problems in variable dimension. Concretely, we aim to optimize f(Wx) over a set F = P ∩ Z, where f ...

Abstract In recent years there has been growing interest in generating valid inequalities for mixedinteger programs using sets with 2 or more constraints. In particular, Andersen et al. (2007) and Borozan and Cornuéjols (2007) study sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach...

In the recent paper Communications in Nonlinear Science and Numerical Simulation. Vol.18. No.11. (2013) 2945-2948, it was demonstrated that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. It was proved that all fractional derivatives Dα, which satisfy the Leibniz rule Dα(fg) = (Dαf) g+ f (Dαg), should have the integer order α = 1, i.e. fraction...

Multiplication of two numbers represented in base is shown to be computable by an on-line algorithm when is a negative integer, a positive non-integer real number, or a complex number of the form ipr, where r is a positive integer.