A satissability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satissability problem, its constraint set deenes an integral polytope if and only if the constraint sets of the set covering problems do. In this sense, resolution reduces the integrality question for the satissability problem to tha...

We show that the class of functions of topologically nontrivial gauge transformations in QCD includes a zero-mode of the Gauss law constraint. The equivalent unconstrained system compatible with Feynman's integral is derived in terms of topological invariant variables, where the zero-mode is identified with the winding number collective variable and leads to the dominance of the Wu-Yang monopol...

The problem of recursive state estimation for a class of distributed parameter systems with an integral quadratic constraint in Hilbert spaces is addressed. Based on solving the linear tracking problem for time-varying systems in Hilbert spaces, necessary and sufficient conditions for robust state estimation problem involving construction of the set of all possible states at the finite interval...

The reduced Ostrovsky equation is a modification of the Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear non-local integral term, which represents the effect of background rotation. This equation is integrable provided a certain curvature constraint is satisfied. We demonstrate, through theoretical analysis and numerical...

In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which ...

The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint w...

We provide preliminary results regarding the existence of a polynomial time approximation scheme (PTAS) for minimizing a linear function over a 0/1 covering polytope which is integral, with one additional covering constraint. Our algorithm is based on extending the methods of Goemans and Ravi for the constrained minimum spanning tree problem and, in particular, implies the existence of a PTAS f...

It is well-known that linear constrained model predictive control has a nonlinearity that is continuous and piecewise affine. Under certain feasibility conditions the nonlinearity may be sector bounded and shown to satisfy sufficient conditions for the existence of Zames-Falb multipliers. Thus the nonlinearity satisfies a wide class of integral quadratic constraint (IQC). Standard analysis then...

We consider a simple action for a fractional spin particle and a path integral representation for the propagator is obtained in a gauge such that the constraint embodied in the Lagrangian is not an obstacle. We obtain a propagator for the particle in a constant electromagnetic field via the path integral representation over velocities, which is characterized by arbitrary boundary conditions and...

This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions. This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints. The integral constraint is included in the cost by a penalty term whereas the bilateral control constraints are handled explicit...