In Biś et al. (Commun Math Phys 394:215–256, 2022) it was stated that the entropy-like map provided by variational principle established in (2022, Theorem 1) is always affine. this note we present an example which shows claim incorrect, and establish necessary sufficient conditions for affinity to hold.

We give a complete characterization of the relationship between shape Euclidean polygon and symbolic dynamics its billiard flow. prove that only pairs tables can have same bounce spectrum are right-angled differ by an affine map. The main tool is new theorem establishes flat cone metric completely determined support Liouville current.

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular W-algebras both in type A. The construction is given via coproduct and evaluation map for Yangians. As a consequence, we show that parabolic inductions representations can be regarded as tensor product under homomorphisms. same method applicable also super-setting.

Disparity estimation is an ill-posed problem in computer vision. It is explored comprehensively due to its usefulness in many areas like 3D scene reconstruction, robot navigation, parts inspection, virtual reality and image-based rendering. In this paper, we propose a hybrid disparity generation algorithm which uses census based and segmentation based approaches. Census transform does not give ...

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed convex function P and a nonzero affine map, with the proximal mappings of τP , τ > 0, easy to compute. In this case, a direct applic...

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this paper we consider the elementary method of alternating projections (MAP) for solving the sparsity optimization problem without employing ...