Gerardo Arizmendi

This study evaluates the feasibility of implementing water markets and improving decision-making for irrigated agriculture in transboundary water basins. It analyzes the physical and economic potential of cooperation between institutions and users in the face of recurrent water scarcity. The research’s study case is the Conchos River basin in Chihuahua, Mexico, where agriculture accounts for 96% of the state’s water use. The basin, with its four main irrigation districts: 005 Delicias, 090 Ojinaga, 103 Florido, and 113 Alto Conchos, contributes approximately 80% of the volume committed in the 1944 International Boundary and Water Treaty between Mexico and the United States. The methodology integrates Cooperative Game Theory with Positive Mathematical Programming (PMP) in Python version 3.12 to optimize water allocation. The models consider crop coefficients, yield response to water deficit, and regulatory proposals: water transfer (75% efficiency), fodder production flexibility (10%), and saving 20% of the maximum transferable volume for the treaty. Results show that cooperation between districts allows positive gains to be maintained, even with a 50% reduction in water availability.

We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations of the Lie algebras spin(8), spin(7) and g(2), etc.

It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the groups of unit--norm elements in the algebras of real quaternions, biquaternions (complex quaternions) and dual quaternions, respectively. In this work, we present a unified framework that allows a wider scope on the subject and includes all the classical results related to the action in dimension 3 and 4 of unit--norm elements of the algebras described above and the algebra of split biquaternions as particular cases. We establish a decomposition of unit--norm elements in all cases and obtain as a byproduct a new decomposition of the group rotations in dimension 4.

We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.