Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one proceeds in the opposite way, enlarging the nonlinear system to a system of greater dimension. We discuss how this approach is also fruitful in studying non inte...

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the...

Map Building and Position Estimation are basic tasks in mobile robot navigation with path planning. A method to generate a global map of the vehicle work environment using ultrasonic sensors is developed in this paper. Depending on the physical properties of the walls that form the room where the robot is navigating, sonar sensors show different behaviours. A neural network is utilized to inter...

in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

We investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. As a modal logic it is special since it features a single modal...

We provide a rigorous treatment of continuous limits for various generalizations the pentagram map on polygons in RPd by means quantum calculus. Describing this limit detail case short-diagonal map, we verify that construction yields (2,d+1)-KdV equation, and moreover, Lax form is proved to become representation corresponding KdV system. More generally, introduce χ-pentagram geometric defining ...

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

In the paper, we study real forms of complex generic Neumann system. We prove that are completely integrable Hamiltonian systems. The system is an example more general Mumford characterized by Lax pair (Lℂ(λ), Mℂ(λ)) 2 × matrices, where and Uℂ(λ), Vℂ(λ), Wℂ(λ) suitable polynomials. topology a regular level set moment map form determined positions roots with respect to position values parameters...