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 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...

A companion of Ostrowski's inequality for functions of bounded variation and applications are given.

a companion of ostrowski's inequality for functions of bounded variation and applications are given.

Recently Y. Meyer gave a characterization of the minimizer of the Rudin-OsherFatemi functional in terms of the -norm. In this work we generalize this result to regularization models with higher order derivatives of bounded variation. This requires us to define generalized -norms. We present some numerical experiments to support the theoretical considerations.

The rescue operations for emergency events usually require multiple emergency departments to cooperate with each other to provide effective and efficient resource allocation plans within a short time limit and dynamically adjust the plans as necessary. In the paper, an agent-based resource allocation approach is proposed to automatically allocate rescue resources to concurrent emergency events ...

We give some extensions of the classical chain rule rg(u)] = g 0 (u)ru and of the chain rule for transport operators a rg(u)] = g 0 (u) a ru, a 2 W 1;1 , via an inverse Sard lemma. Coeecients a of bounded variation are also treated in the case of a Vlasov operator.