In this paper, we propose a subnetwork decomposition/combination approach to investigate the single rate 2-pair unicast problem. It is shown that the solvability of a 2-pair unicast problem is completely determined by four specific link subsets, namely, A1,1, A2,2, A1,2 and A2,1 of its underlying network. As a result, an efficient cut-based algorithm to determine the solvability of a 2-pair uni...

Solvabilities of generalized vector variational-type inequalities (GVVTI) are discussed in this work. First, the solvability of GVVTI without monotone assumption for mappings is considered in (reflexive) Banach spaces by using Brouwer fixed point theorem (Browder fixed point theorem). Second, the solvability of GVVTI with monotone assumption for mappings is considered in reflexive Banach spaces...

The present paper discusses the relations between regularity, Dirichlet, and Neumann problems. Among other results, we prove that the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem for general elliptic operators with complex bounded measurable coefficients. This is strikingly different from the case of real operators, for which such an implica...

Abst rac t . The Genericity Lemma is one of the most important motivations to take in the untyped lambda calculus the notion of solvability as a formal representation of the informal notion of undefinedness. We generalise solvability towards typed lambda calculi, and we call this generalisation: usability. We then prove the Genericity Lemma for un-usable terms. The technique of the proof is bas...

In this paper, we study the problem of feedback complete linearization for a given single input single output stochastic nonlinear system. Using the invariance under transformation rule [1], the coordinate free necessary and su± cient conditions for the solvability of the problem is derived, which is exactly the same as the necessary and su± cient conditions for the solvability of the feedback ...

In recent empirical studies we have shown that many interesting cost-based abduction problems can be solved efficiently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network flow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction ...

We show that serial cost sharing for heterogeneous goods [4], and a large number of other cost sharing mechanisms, have the same strong strategic properties as serial cost sharing for homogenous goods [10], including uniqueness of the Nash equilibrium for all utility profiles and cost functions, dominance solvability, solvability in overwhelmed actions, and robustness to coalitional deviations....

In this paper we study the solvability of a general nD partial control problem in the behavioral framework. This turns out to be characterized in terms of the solvability of another (full) control problem based on a canonical controller associated to the original problem. Moreover we investigate the performance of the canonical controller in achieving a given control objective and generalize th...

In this paper we study the dynamic disturbance decoupling problem for nonlinear discrete-time systems that are considered in a neighbourhood of a given reference trajec-tory. Furthermore the connection between the solvability of this problem and the solvability of the corresponding problem for the time-varying linear discrete-time system obtained by linearizing the original system along the giv...

Abstract: We shall make an overview about fusion categories and some classes of examples related to finite groups. We shall discuss the notions of nilpotency and solvability of a fusion category introduced in the work of Etingof, Gelaki, Nikshych and Ostrik. Then we shall present some results on the solvability of braided fusion categories with Frobenius-Perron dimensions of simple objects $\le...