Related papers: Maximal twisted Betti numbers of complex hyperplan…

This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…

A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…

We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…

We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the…

We study the expected behavior of the Betti numbers of arrangements of the zeros of random (distributed according to the Kostlan distribution) polynomials in $\mathbb{R}\mathrm{P}^n$. Using a random spectral sequence, we prove an…

We show that the system is locally wellposed in by establishing a new commutator estimate

Given a max-plus linear system and a semimodule, the problem of computing the maximal controlled invariant subsemimodule is still open to this day. In this paper, we consider this problem for the specific class of fully actuated systems and…

The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization…

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those…

We construct an additional independent integral of motion for a class of three dimensional minimally superintegrable systems with constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages]…

We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a…

We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier by us in [Math. Z. 274, (2013), no. 3-4, pp. 809-819; arXiv:1009.4488]. We show…

Motivated by the study of area laws for the entanglement entropy of gapped ground states of quantum spin systems and their stability, we prove that the unitary cocycle generated by a local time-dependent Hamiltonian can be approximated, for…

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…

A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state…

The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.

Recently, Chen et al introduced an alternative form of Hardy's paradox for $2$-settings and high-dimensional systems [Phy. Rev. A 88, 062116 (2013)], in which there is a great progress in improving the maximum probability of the nonlocal…

We prove a conjecture by Bravyi on an upper bound on entanglement rates of local Hamiltonians. We then use this bound to prove the stability of the area law for the entanglement entropy of quantum spin systems under adiabatic and…