Related papers: Microlocal Projector for Complete Flow
We consider projections of planar self-similar sets, and show that one can create nonempty interior in the projections by applying arbitrary small perturbations, if the self-similar set satisfies the open set condition and has Hausdorff…
We set the foundation and formulate the Perfect (Ideal) Hyperfluid. The latter represents the natural generalization of the usual perfect fluid structure where now the microscopic characteristics of matter (spin, shear, dilation) are also…
We prove that every projective special K\"ahler manifold with \emph{regular boundary behaviour} is complete and defines a family of complete quaternionic K\"ahler manifolds depending on a parameter $c\ge 0$. We also show that, irrespective…
Reflecting light to a pre-determined non-specular direction is an important ability of metasurfaces, which is the basis for a wide range of applications (e.g., beam steering/splitting and imaging). However, anomalous reflection with 100%…
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…
We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are…
To apply optical flow in practice, it is often necessary to resize the input to smaller dimensions in order to reduce computational costs. However, downsizing inputs makes the estimation more challenging because objects and motion ranges…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
Prototype optical microscopes, built to pursue developments in advanced imaging techniques, need specific optomechanical constructions: preferably with high flexibility in the elements arrangement, easy access to the optical paths,…
In this article we introduce a gluing orbit property, weaker than specification, for both maps and flows. We prove that flows with the $C^1$-robust gluing orbit property are uniformly hyperbolic and that every uniformly hyperbolic flow…
We present design of an all-optical diode in a metal-dielectric structure where plasmonic attenuation and quasi-phase-matching (QPM) is harnessed to improve its performance greatly. Due to the anti-symmetric design of the nonlinear…
We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular…
In this paper we prove an explicit formula for the Bernstein projector to representations of depth at most r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal…
We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…
Many optimal control problems exhibit a peculiar behavior that is not completely understood, the Fuller Phenomenon. In a naive way, this phenomenon can be described as the accumulation of discontinuities in the control function. In this…
We demonstrate perfect imaging in Maxwell's fish eye for microwaves. Our data show that the field of a line source is imaged with subwavelength resolution over superwavelength distances, provided the field is allowed to leave through…
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a…
The purpose of this paper is to prove the finiteness theorems for meromorphic mappings of a complete connected K\"{a}hler manifold into projective space sharing few hyperplanes in subgeneral position without counting multiplicity, where all…