Related papers: Supersolvable resolutions of line arrangements
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry,…
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
It was shown in Alur et al. [1] that the problem of verifying finite concurrent systems through Linearizability is in EXPSPACE. However, there was still a complexity gap between the easy to obtain PSPACE lower bound and the EXPSPACE upper…
We derive several new bounds for the problem of difference sets with local properties, such as establishing the super-linear threshold of the problem. For our proofs, we develop several new tools, including a variant of higher moment…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
It is shown that all PDM Schroedinger equations admitting more than five dimensional Lie symmetry algebras (whose completed list can be found in paper~[{\it J.~Math. Phys.} {\bf 58}, , 083508 (2017)] are exactly solvable. The corresponding…
In this note, we show that real line arrangements of type at most one, admitting only intersection points of multiplicity at most five, satisfy certain boundedness properties. In particular, we prove that a free real arrangement of $d$…
We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal nonlinear potential theory. We provide several fine properties…
In this note we find a bound for the so-called global linear Harbourne constants for smooth hypersurfaces in $\mathbb{P}^{3}_{\mathbb{C}}$
Some posets of binary leaf-labeled trees are shown to be supersolvable lattices and explicit EL-labelings are given. Their characteristic polynomials are computed, recovering their known factorization in a different way.
This paper has been withdrawn by the authors due to a crucial computational error. In this paper we deal with the finite case. We prove that a finite bounded ordered set can be represented as the order of principal congruences of a finite…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.