We study inverse-Monge assignment games, namely cooperative assignment games in which the assignment matrix satisfies the inverse Monge property. For square inverse-Monge assignment games, we describe their cores and we obtain a closed formula for the buyers-optimal and the sellers-optimal core allocations. We also apply the above results to solve the non-square case.

The eigenspace structure for a given n × n concave Monge matrix in a max-plus algebra is described. Based on the description, an O(n) algorithm for computing the eigenspace dimension is formulated, which is faster than the previously known algorithms. Analogous results for convex Monge matrices have been published in [M. Gavalec, J. Plavka, Structure of the eigenspace of a Monge matrix in max-p...

Dispersive deformations of the Monge equation uu = uux are studied using ideas originating from topological quantum field theory and the deformation quantization programme. It is shown that, to a high-order, the symmetries of the Monge equation may also be appropriately deformed, and that, if they exist at all orders, they are uniquely determined by the original deformation. This leads to eithe...

We present the exact solution to the non linear Monge differential equation λ(x, t)λx(x, t) = λt(x, t). It is widely accepted that the Monge equation is equivalent to the ODE .. X= 0 of free motion for particular conditions. Furthermore, the Monge Type equations are connected withX = F ( . X, X; t), which can be integrated with quadratures [1]. Other asymptotic solutions are discussed, see e.g....

We prove several approximation theorems of the complex Monge-Ampère operator on a compact Kähler manifold. As an application we give a simple proof of a recent result of Guedj and Zeriahi on a complete description of the range of the complex Monge-Ampère operator in E(X,ω), which is the class of ω-plurisubharmonic functions with vanishing complex Monge-Ampère mass on all pluripolar sets. We als...

The space of Monge-Ampère functions is a rather large function space with the property that, if u is a Monge-Ampère function, then the determinant of the Hessian can be identified with a well-defined Radon measure, denoted DetDu. Moreover, the map u 7→ DetDu is continuous in a natural weak topology on the space of Monge-Ampère functions. These properties make Monge-Ampère functions potentially ...

Using an example of the galaxy, an attempt is made to explain the flat rotational curves of gas and plasma in galaxies by means of the Ampere force. Using acceptable models for the galactic magnetic field and plausible physical parameters, we find that the flat rotational curves for gas and plasma can be obtained based purely on the observed baryonic (visible) matter distribution and the ampere...