We study the contraction properties of a class of quasi-posterior distributions Π̌n,d obtained by combining a quasi-likelihood function and a sparsity inducing prior distribution on R, as both n (the sample size), and d (the dimension of the parameter) increase. We derive two general results that highlight a set of sufficient conditions under which Π̌n,d puts increasingly high probability on spar...

In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and then use the theory to obtain convergence results for practical adaptive finite element methods (AFEM) applied to several classes of nonlinear elliptic equations. In the first part of the paper, we develop a weak-* convergence fra...

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

Abstract Background: Insufficient uterine activity or hypotonic uterine contraction is a common reason and the cause of abnormal labor progress that can be corrected with oxytocin. Realizing this fact that undue prolongation of labor may contribute to prenatal morbidity has resulted in using oxytocin infusion in different kinds of ineffective uterine contractions. Materials and methods: In th...

proprioceptive neuromuscular facilitation (pnf) training (contraction - relaxation method), in compared to the other methods of static and dynamic stretching exercises; has higher and safer effects on enhancement of hamstring muscle's flexibility, strength and endurance. achieving the optimal combination of contraction and stretching phases in pnf training that can increase these factors of phy...

We prove convergence of adaptive finite element methods (AFEM) for general (nonsymmetric) second order linear elliptic PDE, thereby extending the result of Morin et al [6, 7]. The proof relies on quasi-orthogonality, which accounts for the bilinear form not being a scalar product, together with novel error and oscillation reduction estimates, which now do not decouple. We show that AFEM is a co...

We examine adaptive finite element methods (AFEM) with any polynomial degree satisfying rather general assumptions on the a posteriori error estimators. We show that several non-residual estimators satisfy these assumptions. We design an AFEM with single Dörfler marking for the sum of error estimator and oscillation, prove a contraction property for the so-called total error, namely the scaled ...