Temperature Dependence of 1H Paramagnetic Chemical Shifts in Actinide Complexes,Beyond Bleaney's Theory: The AnVIO22+–Dipicolinic Acid Complexes (An=Np,Pu) as an Example

Actinide +VI complexes ( = , and ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, and complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans’ method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the complex. The temperature dependence of the pNMR chemical shifts has a strong contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the complex and a non-Kramers-doublet model for the complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.     

Variation Operators for Semigroups and Riesz Transforms on BMO in the Schrödinger Setting

In this paper we prove that the variation operators of the heat semigroup and the truncations of Riesz transforms associated to the Schrödinger operator are bounded on a suitable BMO type space.     

Wavelet expansions forBMOρ (w)‐functions

We give necessary and sufficient conditions on the wavelet coefficients of a function for being a member of some BMO_φ (w) space. We achieve this characterization for a wide variety of wavelet systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse minimum flow problem

In this paper we consider the inverse minimum flow (ImF) problem, where lower and upper bounds for the flow must be changed as little as possible so that a given feasible flow becomes a minimum flow. A linear time and space method to decide if the problem has solution is presented. Strongly and weakly polynomial algorithms for solving the ImF problem are proposed. Some particular cases are studied and a numerical example is given.     

A Look at BMOϕ(ω) through Carleson Measures

As Fefferman and Stein showed, there is a tight connection between Carleson measures and BMO functions. In this work we extend this type of results to the more general scope of the BMO_ϕ(ω) spaces. As a byproduct a weighted version of the Triebel-Lizorkin space is introduced, which turns out to be isomorphic to BMO(ω) as in the unweighted case.     

Global W 2, p estimates for nondivergence elliptic operators with potentials satisfying a reverse H?lder condition

In this article, we give some a priori ${L^{p}(\mathbb{R}^{n})}$ estimates for elliptic operators in nondivergence form with VMO coefficients and a potential V satisfying an appropriate reverse H?lder condition, generalizing previous results due to Chiarenza?CFrasca?CLongo to the scope of Schr?dinger-type operators. In particular, our class of potentials includes unbounded functions such as nonnegative polynomials. We apply such a priori estimates to derive some global existence and uniqueness results under some additional assumptions on V.     

Weighted inequalities and a.e. convergence for Poisson integrals in light-cones

We show that the Poisson maximal operator for the tube over the light-cone, P ^*, is bounded in the weighted space L ^p (w) if and only if the weight w(x) belongs to the Muckenhoupt class A _p . We also characterize with a geometric condition related to the intrinsic geometry of the cone the weights v(x) for which P ^* is bounded from L ^p (v) into L ^p (u), for some other weight u(x) > 0. Some applications to a.e. restricted convergence of Poisson integrals are given.     

BMO spaces related to Laguerre semigroups

For the system of Laguerre functions we define a suitable BMO space from the atomic version of the Hardy space considered by Dziubański in 7 , where is the maximal operator of the heat semigroup associated to that Laguerre system. We prove boundedness of over a weighted version of that BMO, and we extend such result to other systems of Laguerre functions, namely and . To do that, we work with a more general family of weighted BMO‐like spaces that includes those associated to all of the above mentioned Laguerre systems. In this setting, we prove that the local versions of the Hardy‐Littlewood and the heat‐diffusion maximal operators turn to be bounded over such family of spaces for weights. This result plays a decisive role in proving the boundedness of Laguerre semigroup maximal operators.