This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems are established for this class of nonlinear projection equations. We utilize one of the alternative theorems to establish several ne...

We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaran...

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including ordinary Hamiltonian G-spaces, Lu’s momentum maps of Poisson group actions, and the group-valued momentum maps of Alekseev–Malkin–Meinrenken. More precisely, we carry out the following program: (1) We de...

We give a partial “quasi-stratification” of the secant varieties of the order d Veronese variety Xm,d of P. It covers the set σt(Xm,d) † of all points lying on the linear span of curvilinear subschemes of Xm,d, but two “quasi-strata” may overlap. For low border rank two different “quasi-strata” are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of ...

Recently quasi-Monte Carlo algorithms have been successfully used for multivariate integration of high dimension d, and were signiicantly more eecient than Monte Carlo algorithms. The existing theory of the worst case error bounds of quasi-Monte Carlo algorithms does not explain this phenomenon. This paper presents a partial answer to why quasi-Monte Carlo algorithms can work well for arbitrari...

We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of b frequencies, b ≤ d + 2, in arbitrary dimension d and for arbitrary non integrable algebraic nonlinearity p. This reflects the conservation of d momenta, energy and L norm. In 1d, we prove the existence of quasi-periodic solutions with arbit...

we shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a p-invariant measure m for Q to be p-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. @ 2000 Elsevier Science Ltd. All rights reserv...

In previous investigations into the subject ([4], [9], [1]), p 0 quasi-MV algebras have been mainly viewed as preordered structures w.r.t. the induced preorder relation of their quasi-MV term reducts. In this paper, we shall focus on a di¤erent relation which partially orders cartesian p 0 quasi-MV algebras. We shall prove that: a) every cartesian p 0 quasi-MV algebra is embeddable into an inte...