We consider the connected variant of the classic mixed search game where, in each search step, cleaned edges form a connected subgraph. We consider graph classes with bounded connected monotone mixed search number and we deal with the the question weather the obstruction set, with respect of the contraction partial ordering, for those classes is finite. In general, there is no guarantee that th...

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = σtZt, where the unobservable volatility σt is a parametric function of (Xt−1, . . . ,Xt−p, σt−1, . . . , σt−q) for some p, q ≥ 0, and (Zt) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equatio...

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = σtZt , where the unobservable volatility σt is a parametric function of (Xt−1, . . . ,Xt−p,σt−1, . . . , σt−q) for some p,q ≥ 0, and (Zt ) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equatio...

The Ludvigsen–Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius r about a point o. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common...

In this paper we provide approximate analytical analysis of stability of nonsingular inflationary chaotic-type cosmological models. Initial conditions for nonsingular solutions at the bounce correspond to dominance of potential part of the energy density of the scalar field over its kinetic part both within general relativity and gauge theories of gravity. Moreover, scalar field at the bounce e...

A number of works concerning rigorous convergence theory for adaptive finite element methods (AFEM) for controlling global energy errors have appeared in recent years. However, many practical situations demand AFEM designed to efficiently compute quantities which depend on the unknown solution only on some subset of the overall computational domain. In this work we prove convergence of an adapt...