Equilibrium and NMR studies on GdIII, YIII, CuII and ZnII complexes of various DTPA-N,N'-bis(amide) ligands. Kinetic stabilities of the gadolinium(III) complexes

Three DTPA-derivative ligands, the non-substituted DTPA-bis(amide) (L(0)), the mono-substituted DTPA-bis(n-butylamide) (L(1)) and the di-substituted DTPA-bis[bis(n-butylamide)] (L(2)) were synthesized. The stability constants of their Gd3+ complexes (GdL) have been determined by pH-potentiometry with the use of EDTA or DTPA as competing ligands. The endogenous Cu2+ and Zn2+ ions form ML, MHL and M(2)L species. For the complexes CuL(0) and CuL(1) the dissociation of the amide hydrogens (CuLH(-1)) has also been detected. The stability constants of complexes formed with Gd3+, Cu2+ and Zn2+ increase with an increase in the number of butyl substituents in the order ML(0) < ML(1) < ML(2). NMR studies of the diamagnetic YL(0) show the presence of four diastereomers formed by changing the chirality of the terminal nitrogens of their enantiomers. At 323 K, the enantiomerization process, involving the racemization of central nitrogen, falls into the fast exchange range. By the assignment and interpretation of 1H and 13C NMR spectra, the fractions of the diastereomers were found to be equal at pH = 5.8 for YL(0). The kinetic stabilities of GdL(0), GdL(1) and GdL(2) have been characterized by the rates of the exchange reactions occurring between the complexes and Eu3+, Cu2+ or Zn2+. The rates of reaction with Eu3+ are independent of the [Eu3+] and increase with increasing [H+], indicating the rate determining role of the proton assisted dissociation of complexes. The rates of reaction with Cu2+ and Zn2+ increase with rising metal ion concentration, which shows that the exchange can take place with direct attack of Cu2+ or Zn2+ on the complex, via the formation of a dinuclear intermediate. The rates of the proton, Cu2+ and Zn2+ assisted dissociation of Gd3+ complexes decrease with increasing number of the n-butyl substituents, which is presumably the result of steric hindrance hampering the formation or dissociation of the intermediates. The kinetic stabilities of GdL(0) and GdL(1) at pH = 7.4, [Cu2+] = 1 x 10(-6) M and [Zn(2+)] = 1 x 10(-5) M are similar to that of Gd(DTPA)2-, while the complex GdL2 possesses a much higher kinetic stability.     

Quasiorder lattices of varieties

The set \({{\mathrm{Quo}}}(\mathbf {A})\) of compatible quasiorders (reflexive and transitive relations) of an algebra \(\mathbf {A}\) forms a lattice under inclusion, and the lattice \({{\mathrm{Con}}}(\mathbf {A})\) of congruences of \(\mathbf {A}\) is a sublattice of \({{\mathrm{Quo}}}(\mathbf {A})\). We study how the shape of congruence lattices of algebras in a variety determine the shape of quasiorder lattices in the variety. In particular, we prove that a locally finite variety is congruence distributive [modular] if and only if it is quasiorder distributive [modular]. We show that the same property does not hold for meet semi-distributivity. From tame congruence theory we know that locally finite congruence meet semi-distributive varieties are characterized by having no sublattice of congruence lattices isomorphic to the lattice \(\mathbf {M}_3\). We prove that the same holds for quasiorder lattices of finite algebras in arbitrary congruence meet semi-distributive varieties, but does not hold for quasiorder lattices of infinite algebras even in the variety of semilattices.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

Karhunen–Loève expansion for a generalization of Wiener bridge

We derive a Karhunen–Loève expansion of the Gauss process \( {B}_t-g(t){\int}_0^1{g}^{\hbox{'}}(u)\mathrm{d}{B}_u,t\in \left[0,1\right] \), where (B_t)_t?∈?[0,?1] is a standardWiener process, and g?:?[0,?1]?→?? is a twice continuously differentiable function with g(0) = 0 and \( {\int}_0^1{\left(g\hbox{'}(u)\right)}^2\mathrm{d}u=1 \). This process is an important limit process in the theory of goodness-of-fit tests. We formulate two particular cases with the functions \( g(t)=\left(\sqrt{2}/\pi \right)\sin \left(\pi t\right),t\in \left[0,1\right] \), and g(t)?=?t, t?∈?[0,?1]. The latter corresponds to the Wiener bridge over [0, 1] from 0 to 0.     

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

High-pressure NMR study of water exchange on magnetic resonance imaging contrast agents

Abstract

The knowledge of water exchange reaction mechanism in aqueous solutions of Gd³⁺ polyaminocarboxylates is important for the understanding of the relatively slow water exchange rates measured for these complexes. Variable ressure measurements show a change of mechanism from associatively activated on [Gd(H₂O)₈]³⁺ and [Gd(PDTA)(H₂O₂)₂]^? to probably limiting dissociative on the MRI contrast agents [Gd(DOTA)(H₂O)]^?, [Gd(DTPA)(H₂O)]^2? and [Gd(DTPA-BMA)(H₂O)].     

Galvanostatic charge–discharge tests, 57Fe and 119Sn Mössbauer and XRD measurements on novel Sn-Ni-Fe electrodeposits

Novel Sn–Ni–Fe ternary alloys were successfully deposited by pulse plating technique from an electrolyte based on sodium gluconate which acts as a complexing agent. XRD results revealed the predominantly amorphous character for the majority of the deposits. ⁵⁷Fe and ¹¹⁹Sn conversion electron Mössbauer spectroscopy indicated the formation of a paramagnetic amorphous alloy using a short on-pulse duration and where the Fe content was less than 22 wt.%. Galvanostatic charge–discharge tests of the novel Sn-Ni-Fe deposits were carried out in a model Li-ion cell and indicated that the Sn-Ni-Fe alloys have potential as an electrode material.     

Improving the visible-light photocatalytic activity of SnO<Subscript>x</Subscript>·SiO<Subscript>2</Subscript> glass systems by introducing SnO<Subscript>x</Subscript> nanoparticles

Tin silicate glass without SnO_x nanoparticles (SiO₂·SnO_x), a silica glass containing only SnO_x nanoparticles (SiO₂·SnO_xNP) and the improved product, which combines the tin silicate glass with SnO_x nanoparticles (SiO₂·SnO_x·SnO_xNP) was prepared. For the structural analysis ¹¹⁹Sn Mössbauer spectroscopy and X-ray diffraction were applied. The ¹¹⁹Sn Mössbauer spectra showed that the SiO₂·SnO_x·SnO_xNP sample had the largest Sn^II content (12.0%). It also had an outstanding methylene blue degradation with the first-order rate value with (18?±?2) × 10^?3 min^?1 with visible light irradiation.     

Densest Geodesic Ball Packings to <Emphasis Type="Bold">S</Emphasis><Superscript>2</Superscript> × <Emphasis Type="Bold">R</Emphasis> space groups generated by screw motions

In this paper we study the locally optimal geodesic ball packings with equal balls to the S ² × R space groups having rotation point groups and their generators are screw motions. We determine and visualize the densest simply transitive geodesic ball arrangements for the above space groups; moreover, we compute their optimal densities and radii. The densest packing is derived from the S ² × R space group 3qe. I. 3 with packing density ≈0.7278. E. Molnár has shown in [9] that the Thurston geometries have an unified interpretation in the real projective 3-sphere \({\mathcal{PS}^3}\). In our work we shall use this projective model of S ² × R geometry.