We present a consistent and comprehensive treatise on the foundations of the extended HamiltonLagrange formalism—where the dynamical system is parameterized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables q(s). In the action principle, the conventional classical action L dt is then...

In high-level constraint modelling languages, constraints can occur in non-Boolean contexts: implicitly, in the form of partial functions, or more explicitly, in the form of constraints on local variables in non-Boolean expressions. Specifications using these facilities are often more succinct. However, these specifications are typically executed on solvers that only support questions of the fo...

The Object Constraint Language OCL is an integral part of UML, the Unified Modeling Language standard. It has been added to Rational’s UML core as a logic-based sublanguage for the definition of integrity constraints (invariants) on class diagrams as well as for the definition of preand postconditions of operations. Despite of the fact that OCL is called a statically typed language its type che...

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the val...

A functional integral formalism is used to derive the extension of a stiff chain subject to an external force. The force versus extension curves are calculated using a mean-field approach in which the hard constraint u(s)51 is replaced by a global constraint ^u(s)&51 where u(s) is the tangent vector describing the chain and s is the arclength. The theory quantitatively reproduces the experiment...

This paper presents a practical model for load frequency control (LFC) of two-area interconnected power system. The proposed model is a non-linear power system and is framed with thermal generating units including security constraint governor dead band imposed by the governor. A Proportional Integral Derivative (PID) controller is used for the design and analysis of the proposed model. The Part...

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with a cosmological constant. The construction amplitudes uses the state-integral model $\mathrm{PSL}(2,\mathbb{C})$ Chern-Simons theory and implementation simplicity constraint. has two key features: (1) are all finite, (2) suitable boundary data, semiclassical asymptotics vertex amplitude oscillatory terms...

Existence of optimal solutions and necessary optimality conditions for a controlled version Moreau's sweeping process are derived. The control is measurable ingredient the dynamics constraint set polyhedron. novelty consists in considering time periodic trajectories, adding requirement that have zero average, an integral functional lacks weak semicontinuity. A model coming from locomotion soft-...

Computation of general stateand/or control-constrained Optimal Control Problems (OCPs) is difficult for various constraints, especially the intractable path constraint. For such problems, the theoretical convergence of numerical algorithms is usually not guaranteed, and the right solution may not be successfully obtained. With the recently proposed Variation Evolving Method (VEM), the evolution...

Boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities. In addition, surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics. This makes the spatial discretization even more difficult and, at the same time, imposes a severe time step constraint for stable explicit time integration methods. A proof ...