Related papers: Some Open Problems Related to Stability
The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.
Organizations continuously accumulate data, often according to some business processes. If one poses a query over such data for decision support, it is important to know whether the query is stable, that is, whether the answers will stay…
This is an exposition for mathematicians of some unsolved problems arising in control theory of linear time-independent systems.
Interacting networks are different in nature to single networks. The study of queuing processes on interacting networks is underdeveloped. It presents new mathematical challenges and is of importance to applications. This area of operations…
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in…
I offer a case that quantum query complexity still has loads of enticing and fundamental open problems -- from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current…
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of…
For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this note we briefly survey and propose some open problems related to isoparametric theory.