The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem.

In this longitudinal study, the authors addressed intracultural variation on fathers’ interactions with their 3-month-old infants, their ideas about parental care, and the timing of their children’s self-recognition at the age of 18–20 months. Participants were 24 middle-class German fathers and their firstborn children. Two behavioral clusters emerged: a more proximal parenting style with exte...

(nknl) are established, where (nk)1≤k≤N is any sequence of distinct positive integers and 0 < α ≤ 1; the estimate for α = 1/2 solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for α = 1/2. The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues ...

In this paper, we establish a refinement of the difference between two integral means for functions of bounded variation in terms of the cumulative variation function. The applications for probability density functions are also given.

Chaundy and Jolliffe [1] proved that if {an} is a non-increasing (monotonic) real sequence with lim n→∞ an = 0, then a necessary and sufficient condition for the uniform convergence of the series P∞ n=1 an sinnx is lim n→∞ nan = 0. We generalize (or weaken) the monotonic condition in this well-known result to the so-called mean value bounded variation condition and prove that the generalized co...

We show some estimates and approximation results of operators convolution type de?ned on Riesz Bounded variation spaces in Rn. also state embedding that involve the collection generalized absolutely continuous functions.

Two methods are given for the calculus of the fundamental matrix for the generalized linear differential equations on the Banach space of functions of bounded variation. The main result extends the Peano-Baker formula in this framework.

We present some properties of real valued functions of bounded generalized variation of Riesz–Orlicz type including weight and characterize Lipschitzian superposition Nemytskii operators which map between spaces (in fact, Banach algebras) of these functions.

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...