Expanding the Ligand Classes Used for Mn(II) Complexation: Oxa-aza Macrocycles Make the Difference

We report two macrocyclic ligands based on a 1,7-diaza-12-crown-4 platform functionalized with acetate (tO2DO2A²⁻) or piperidineacetamide (tO2DO2AM^Pip) pendant arms and a detailed characterization of the corresponding Mn(II) complexes. The X−ray structure of [Mn(tO2DO2A)(H₂O)]·2H₂O shows that the metal ion is coordinated by six donor atoms of the macrocyclic ligand and one water molecule, to result in seven-coordination. The Cu(II) analogue presents a distorted octahedral coordination environment. The protonation constants of the ligands and the stability constants of the complexes formed with Mn(II) and other biologically relevant metal ions (Mg(II), Ca(II), Cu(II) and Zn(II)) were determined using potentiometric titrations (I = 0.15 M NaCl, T = 25 °C). The conditional stabilities of Mn(II) complexes at pH 7.4 are comparable to those reported for the cyclen-based tDO2A²⁻ ligand. The dissociation of the Mn(II) chelates were investigated by evaluating the rate constants of metal exchange reactions with Cu(II) under acidic conditions (I = 0.15 M NaCl, T = 25 °C). Dissociation of the [Mn(tO2DO2A)(H₂O)] complex occurs through both proton− and metal−assisted pathways, while the [Mn(tO2DO2AM^Pip)(H₂O)] analogue dissociates through spontaneous and proton-assisted mechanisms. The Mn(II) complex of tO2DO2A²⁻ is remarkably inert with respect to its dissociation, while the amide analogue is significantly more labile. The presence of a water molecule coordinated to Mn(II) imparts relatively high relaxivities to the complexes. The parameters determining this key property were investigated using ¹⁷O NMR (Nuclear Magnetic Resonance) transverse relaxation rates and ¹H nuclear magnetic relaxation dispersion (NMRD) profiles.     

Production of ball-lightning-like luminous balls by electrical discharges in silicon

We performed electric arc discharges in pure Si to generate luminous balls with lifetime in the order of seconds and several properties usually reported for natural ball lightning. This simple experiment does not rely on energy sources and excitation mechanisms that are improbable in the natural phenomenon and clearly demonstrates the role of vaporization and oxidation of Si, as proposed by the Abrahamson-Dinniss theory for ball-lightning formation.     

Isotropic compensation of diffraction-driven angular dispersion

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.     

Gouy wave modes: undistorted pulse focalization in a dispersive medium

Gouy wave modes are linear waves with finite energy that propagate without distortion at any phase and group velocity through a focal region in a dispersive medium. These features make them potentially useful for the onset and control of nonlinear interactions.     

On feedback and stable price adjustment mechanisms

Given an excess demand function of an economy, say Z(p)$Z(p)$, a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,_p0)$p(t,p_0)$ to an equilibrium _peq$p_{\mathit{eq}}$ solution of Z(p)=0$Z(p)=0$. Besides, all equilibrium points of Z(p)$Z(p)$ are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.