Related papers: On the Congruences in Right Loops
In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.
The potential energy of a system in stable equilibrium has a minimum value. This property is used to derive a formula that is useful in determi- nation of stability of a floating body. It is found that a floating body is in stable…
We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in…
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y. Takeuchi, and H. Tokumaru, who, in a series of papers,…
We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…
We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.
The location and width of the time window in which a sequence of processes converges to equilibrum are given under conditions of exponential convergence. The location depends on the side: the left-window and right window cutoffs may have…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
In this paper, which is a follow-up to [A. Borobia, R. Canogar, F. De Ter\'an, Mediterr. J. Math. 18, 40 (2021)], we provide a necessary and sufficient condition for the matrix equation $X^\top AX=B$ to be consistent when $B$ is symmetric.…
In this paper, we give necessary and sufficient conditions for the rigidity of perimeter inequality under Schwarz symmetrisation. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the…
We describe several configurations of clasped ropes which are balanced and thus critical for the Gehring ropelength problem of arXiv:math.DG/0402212.
An examples of solutions of the equation for curvature of congruence of cycles are constructed. Their properties are discussed.
This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones…
We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and we then investigate when these conditions…
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…