Structure and morphology of spinel MFe2O4 (M=Fe, Co, Ni) nanoparticles chemically synthesized from heterometallic complexes

We synthesized magnetic spinel ferrites from trimetallic single-source precursors. Fe(II), Co(II), and Ni(II) ferrite nanoparticles in the range of 9-25 nm were synthesized by solvothermal decomposition of trimetallic acetate complex precursors in benzyl ether in the presence of oleic acid and oleylamine, using 1,2-dodecanediol as the reducing agent. For comparison, spinel ferrite nanoparticles were synthesized by stoichiometric mixtures of metal acetate or acetylacetonate salts. The nanoparticles (NP) were characterized by TEM, DLS, powder XRD, and Raman spectroscopy; and their magnetic properties were characterized by ZFC-FC and M(H) measurements. The ferrite-NP were more homogeneous and had a narrower size distribution when trimetallic complexes were used as precursors. As a consequence, the magnetic properties of these ferrite-NP are closer to the aimed room temperature superparamagnetic behavior, than are those of other ferrites obtained by a mixture of salts.     

Synthesis and physical properties of K4[Fe(C5O5)2(H2O)2](HC5O5)2·4H2O (C5O5(2-) = croconate): a rare example of ferromagnetic coupling via H-bonds

The reaction of the croconate dianion (C(5)O(5))(2-) with a Fe(III) salt has led, unexpectedly, to the formation of the first example of a discrete Fe(II)-croconate complex without additional coligands, K(4)[Fe(C(5)O(5))(2)(H(2)O)(2)](HC(5)O(5))(2)·4H(2)O (1). 1 crystallizes in the monoclinic P2(1)/c space group and presents discrete octahedral Fe(II) complexes coordinated by two chelating C(5)O(5)(2-) anions in the equatorial plane and two trans axial water molecules. The structure can be viewed as formed by alternating layers of trans-diaquabis(croconato)ferrate(II) complexes and layers containing the monoprotonated croconate anions, HC(5)O(5)(-), and noncoordinated water molecules. Both kinds of layers are directly connected through a hydrogen bond between an oxygen atom of the coordinated dianion and the protonated oxygen atom of the noncoordinated croconate monoanion. A H-bond network is also formed between the coordinated water molecule and one oxygen atom of the coordinated croconate. This H-bond can be classified as strong-moderate being the O···O bond distance (2.771(2) ?) typical of moderate H-bonds and the O-H···O bond angle (174(3)°) typical of strong ones. This H-bond interaction leads to a quadratic regular layer where each [Fe(C(5)O(5))(2)(H(2)O)(2)](2-) anion is connected to its four neighbors in the plane through four equivalent H-bonds. From the magnetic point of view, these connections lead to an S = 2 quadratic layer. The magnetic properties of 1 have been reproduced with a 2D square lattice model for S = 2 ions with g = 2.027(2) and J = 4.59(3) cm(-1). This model reproduces quite satisfactorily its magnetic properties but only above the maximum. A better fit is obtained by considering an additional antiferromagnetic weak interlayer coupling constant (j) through a molecular field approximation with g = 2.071(7), J = 2.94(7) cm(-1), and j = -0.045(2) cm(-1) (the Hamiltonian is written as H = -JS(i)S(j)). Although this second model might still be improved since there is also an extra contribution due to the presence of ZFS in the Fe(II) ions, it confirms the presence of weak ferromagnetic Fe-Fe interactions through H-bonds in compound 1 which represents one of the rare examples of ferromagnetic coupling via H-bonds.     

New interferometric technique to evaluate the electric charge of gas bubbles in liquids

We report a new interferometric technique to measure the electric charge at the gas-liquid interface of a bubble in a liquid. The bubble rests by buoyancy against an electrode, and an alternating electric field excites its capillary oscillations. The oscillation amplitude of the quadrupolar mode frequency is measured by the interferometer, and it is used to evaluate the electric charge. The mode frequency scales with the square root of the interfacial tension and with a -(3)/(2) power law as a function of the bubble radius. For bubbles in the millimeter diameter range in pure water, the measured negative charge scales with the square of the radius, hence, giving a constant surface charge density on the order of 1.8 × 10(-5) C m(-2), which is rather consistent with the electrophoretic values reported in the literature.     

The Indian drawings of the poet Cesare Pascarella: non-destructive analyses and conservation treatments

The Italian dialect poet Cesare Pascarella travelled all around the world, noting down in notebooks his keen and caustic observations, and drawing sketches that are a visual reportage of his journeys. The sketches were mounted as a random collage over acidic cardboards that were exposed to direct sunlight in his studio. Their poor state of conservation is related to the use of modern paper: chemical instability of raw materials caused acidification and strong oxidation of the support, with intense yellowing of the surfaces and brittleness of the paper. To ensure future preservation of the drawings, chemical stabilisation with simultaneous alcoholic treatment by deacidification (calcium propionate) and reduction (borane tert-butylamine complex) appeared necessary. To verify its applicability, it was indispensible to characterise the support and identify the nature of all the graphic media. The use of Raman, Infrared, X-ray fluorescence spectroscopies and scanning electron microscopy coupled with X-ray microanalysis allowed us to clear the problems related to the different penetration depth of each analytical technique and the different responses of pigments/dyes to each spectroscopy. The palette, how it varied along the journeys, the different supports used and preparations were completely identified showing a choice of colours compatible with the reduction treatment.     

New serinolic amino-<Emphasis Type="Italic">s</Emphasis>-triazines by chemoselective amination of cyanuric chloride and their (pro)diastereomerism in restricted rotational phenomena

The highly chemoselective preparation of new elaborated N-unsymmetrically substituted chlorodiamino-s-triazines and melamines, seen as building-blocks for iterative synthesis, is reported. It consisted of amination of cyanuric chloride with commercial C-2-substituted 2-aminopropane-1,3-diols (“serinols”), playing the role as “open-chain” unit and enantiopure (1S,2S)-2-amino-1-(4-nitrophenyl)propane-1,3-diols (“p-nitrophenylserinols”) based amino-1,3-dioxanes (“closed-chain” unit). Issued from the restricted rotation about C(s-triazine)-N(exocyclic) partial double bonds, seen as axes of (pro)diastereomerism, a global four-component rotational equilibrium involving the title compounds is discussed based on DFT computation and (VT) NMR data. Depending on π-deficiency of the s-triazine core, an (un)synchronised deblocking of the generated rotational diastereomers was observed. They are discussed as influence of intra-vs. intermolecular NH...OH (dynamic) interactions occurring in the “open-chain” unit and the anancomeric, axial vs. equatorial, amino-anchorage of the “closed-chain” unit.      

On nonatomicity for non-additive functions

The notion of nonatomicity for set functions plays a key role in classical measure theory and its applications. For classical measures taking values in finite dimensional Banach spaces, it guarantees the connectedness of range. Even just replacing σ-additivity with finite additivity for measures requires some stronger nonatomicity property for the same conclusion to hold. In the present paper, we deal with non-additive functions – called ‘s-outer’ and ‘quasi-triangular’ – defined on rings and taking values in Hausdorff topological spaces. No algebraic structure is required on their target spaces. In this context, we make use of a notion of strong nonatomicity involving just the behavior of functions on ultrafilters of their underlying Boolean domains. This notion is proved to be equivalent to that proposed in earlier contributions concerning Lyapunov-types theorems in additive and non-additive frameworks. Thus, in particular, our analysis allows to generalize, improve and unify several known results on this topic.     

Forbidden subgraphs and the König–Egerváry property

The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König–Egerváry property  if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König–Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász’s result to a characterization of all graphs having the König–Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König–Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König–Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.     

New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

Let ψ and φ be analytic functions on the open unit disk $\mathbb{D}$ with φ( $\mathbb{D}$ ) ? $\mathbb{D}$ . We give new characterizations of the bounded and compact weighted composition operators W _ψ,? from the Hardy spaces H ^p , 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A _α ^p , α > ? 1,1 ≤ p < ∞, and the Dirichlet space $\mathcal{D}$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W _ψ,? f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H ¹ as well as of compactness for H ^p , 1 ≤ p < ∞, and $\mathcal{D}$ purely in terms of the symbols ψ and φ.     

Étale cohomology of a DM curve-stack with coefficients in \mathbb G _m

We compute étale cohomology groups $H_{\acute{\mathrm{e}}\mathrm{t}}^r(X, \mathbb G _m)$ in several cases, where $X$ is a connected smooth tame Deligne–Mumford stack of dimension $1$ over an algebraically closed field. We have complete results for orbicurves (and, more generally, for twisted nodal curves) and in the case all stabilizers are cyclic; we give partial results and examples in the general case. In particular, we show that if the stabilizers are abelian then $H_{\acute{\mathrm{e}}\mathrm{t}}^2(X, \mathbb{G }_m)$ does not depend on $X$ but only on the underlying orbicurve $Y$ and on the generic stabilizer. We show with two examples that, in general, the higher cohomology groups $H_{\acute{\mathrm{e}}\mathrm{t}}^r(X, \mathbb{G }_m)$ cannot be computed knowing only the base of the gerbe $X \rightarrow Y$ and the banding group.     

A remark on the <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">1</Emphasis></Superscript>-lower semicontinuity for integral functionals in BV

We study the L ¹ -lower semicontinuity in BV of an integral functional of the type . Our assumptions on f extend previous results recently obtained by Gori, Maggi and Marcellini in the case where the above functional is restricted to W ^1,1 .