This is a report on how mixed integer programming works. It starts by showing the form of a mixed integer program with n variables and m constraints. They explain the branch and bound method which is the most widely used method for solving integer programs. It goes into some detail about how the variables have only two possible restrictions, one and zero. There’s also some mention of the branch...

Solutions of calcium chloride in mixed water and formamide are excellent electrolytes for capacitive charge storage in partially oxidised carbon nanotubes at unprecedented sub-zero-temperatures (e.g. 67% capacitance retention at -60 °C).

This paper studies the mixed zero-sum stochastic differential game problem. We allow functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. show existence solution for this we prove saddle-point game. Moreover, in Markovian framework that value function unique viscosity associated Hamilton–Jacobi–Bellman (H...

The “entanglement of formation” of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two non-zero eigenvalues, and we report evidence suggesting that the form...

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker–Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy Mn models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They ...

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble — the ensemble realizing the entanglement of formation — is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the...

In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are associated with classical nonanticipative strategies (with delay). Imposing on the underlying controls for both players a conditional independence property, we o...