in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...

Much empirical support of self-control theory is based on the 24-item scale conceptualized by Grasmick and his colleagues. This study examined the dimensionality of the scale. Exploratory factor analysis, confirmatory factor analyses, and a structural equation model (SEM) produced results that are discordant with much prior research. The Grasmick et al. scale was not unidimensional, more comple...

A parallel-in-time, multiscale interaction procedure is introduced for systems described at molecular scales by time-dependent random variables that obey Langevin dynamics. At larger, kinetic scales, the system is described by a probability distribution function that obeys an associated Fokker-Planck equation. It is assumed that the main quantity of interest is the kinetic-scale probability dis...

An adaptive discontinuous Galerkin multiscale method driven by an energy norm a posteriori error bound is proposed. The method is based on splitting the problem into a coarse and fine scale. Localized fine scale constituent problems are solved on patches of the domain and are used to obtain a modified coarse scale equation. The coarse scale equation has considerably less degrees of freedom than...

We consider the two-scale refinement equation f(x) = ∑N n=0 cnf(2x − n) with ∑ n c2n = ∑ n c2n+1 = 1 where c0, cN 6= 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn ≥ 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, as well as the cascade algorithm converge unifo...

Let (Ω,A, P ) be a complete probability space. We show that the trivial function is the unique L-solution of the following refinement type equation f(x) = Z Ω |φx(x, ω)|f(φ(x, ω))dP (ω) for a wide class of the given functions φ. This class contains functions of the form φ(x, ω) = α(ω)x−β(ω) with −∞ < R Ω log |α(ω)|dP (ω) < 0.