We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ √ iS] rather t...

We consider an evasion differential game of many pursuers and one evader with integral constraints in the plane. The game is described by simple equations. Each component of the control functions of players is subjected to integral constraint. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on cont...

This paper reviews the contrast source inversion method as a robust algorithm to solve the nonlinear inverse scattering problem, where the discrepancy between the measured and predicted scattered field data is minimized. The algorithm is based on a source type of integral representation of the scattered field, where the integral operator acts on a contrast source, being the product of the inter...

We study energy transfer in unbounded Charney-Hasegawa-Mima and surface quasigeostrophic turbulence. The possible inverse-cascading quantities in these systems are, respectively, I identical with integral ( infinity )(0)k(-2)E(k) dk and J identical with integral ( infinity )(0)k(-1)E(k) dk, where E(k) is the kinetic energy spectrum. The supposed direct-cascading quantities for both surface quas...

It is well-known that the intersection of the matching polytope with a cardinality constraint is integral [8]. We prove a similar result for the polytope corresponding to the transportation problem with market choice (TPMC) (introduced in [4]) when the demands are in the set {1, 2}. This result generalizes the result regarding the matching polytope and also implies that some special classes of ...

A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decision-maker's actions) that satisfies a series of axioms pertaining to decision-maker's behavior, is established. The obtained utility is a gene...

A careful reexamination of the quantization of systems with firstand second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional treatments. Most significantly, we emphasize the importance of using path-integral measures for Lagrange multipliers which ensure that the quantum system satisfies the q...

k-submodular functions, introduced by Huber and Kolmogorov, are functions defined on {0, 1, 2, . . . , k}n satisfying certain submodular-type inequalities. k-submodular functions typically arise as relaxations of NP-hard problems, and the relaxations by k-submodular functions play key roles in design of efficient, approximation, or FPT algorithms. Motivated by this, we consider the following pr...

This paper addresses a problem of set-valued state estimation for uncertain continuous-time systems via limited capacity communication channels. The uncertainty of the systems satisfies an integral quadratic constraint. Using results from the robust Kalman filtering, we design a coder/decoder-estimator pair that allows us to construct set-valued state estimate of the systems via communication c...

The paper considers a model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint and the uncertain system has zero initial condition. This leads to a method for model validation which is based around a robust Kalman filter type structure.