On the finiteness of optimal partitions

We prove that, under appropriate assumptions on the domain Ω and on the datumg, any optimal partition of Ω (minimizing the sum of the total perimeter and the approximation term is finite. Finiteness result for the problem of image segmentation in Artificial Vision can be deduced.

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Sunto Dimostriamo che, in opportune ipotesi sul dominio Ω e sul datog, ogni partizione ottimale di Ω (minimizzante il perimetro totale in Ω più il termine di approssimazione è finita. Se ne deducono risultati di finitezza per il problema della segmentazione di immagini in Visione Artificiale.

     

Reactions of 1,4-diaza-3-methylbutadien-2-ylpalladium(II) derivatives with chloro-bridged rhodium(I) complexes

The reactions of the organometallic 1,4-diazabutadienes, RN=C(R′)C(Me)=NR″ [R = R″ = p-C₆H₄OMe, R′ = trans-PdCl(PPh₃)₂ (DAB); R = p-C₆H₄OMe, R″ = Me, R′ = trans-PdCl(PPh₃)₂ (DAB^I; R = R″ = p-C₆H₄OMe, R′ = Pd(dmtc)-(PPh₃), dmtc = dimethyldithiocarbamate (DAB^II); R = R″ = p-C₆H₄OMe, R′ = PdCl(diphos), diphos = 1,2-bis(diphenylphosphino)ethane (DAB^III)] with [RhCl(COD)]₂ (COD = 1,5-cyclooctadiene, Pd/Rh ratio = $\text{1}\text{2}$) depend on the nature of the ancillary ligands at the Pd atom in group R′. In the reactions with DAB and DAB^I transfer of one PPh₃ ligand from Pd to Rh occurs yielding [RhCl(COD)(PPh₃)] and the new binuclear complexes [Rh(COD) {RN=C(R?)-C(Me)=NR″}], in which the diazabutadiene moiety acts as a chelating bidentate ligand. Exchange of ligands between the two different metallic centers also occurs in the reaction with DAB^II. In this case, the migration of the bidentate dmtc anion yields [Rh(COD)Pdmtc] and [Rh(COD) {RN=C(R?)C(Me)=NR″}]. In contrast, the reaction with DAB^III leads to the ionic product [Rh(COD)- (DAB^III)][RhCl₂(COD)], with no transfer of ligands. The cationic complex [Rh(COD)(DAB^III)]⁺ can be isolated as the perchlorate salt from the same reaction (Pd/Rh ratio = 1/1) in the presence of an excess of NaClO₄. In all the binuclear complexes the coordinated 1,5-cyclooctadiene can be readily displaced by carbon monoxide to give the corresponding dicarbonyl derivatives. The reaction of [RhCl(CO)₂]₂ with DAB and/or DAB^I yields trinuclear complexes of the type [RhCl(CO)₂]₂(DAB), in which the diazabutadiene group acts as a bridging bidentate ligand. Some reactions of the organic diazabutadiene RN=C(Me)C(Me)=NR (R = p-C₆H₄OMe) are also reported for comparison.     

Intercalation of α,ω-alkyldiamines in layered α-zirconium phosphate and the inclusion behaviour of some of the intercalates obtained

The paper reports a study on the intercalation mechanism of NH₂(CH₂) _n NH₂ (withn=2, 4, 6, 8, 10) diamines in layered Zr(HOPO₃)₂·H₂O, performed by titrating the host with aqueous solutions of amines at 80°C. The intercalation reactions occur stepwise according to the ‘moving boundary’ model, with the formation of a number of intermediate intercalation compounds of formula Zr(HOPO₃)₂·xNH₂(CH₂) _n NH₂ (0<x<1) before obtaining the fully intercalated ones (x=1). For each diamine the batch titration curve and a diagram of the phases involved in the interaclation reaction are reported. Twenty-two intercalation compounds have been isolated and characterized by their composition, XRD patterns and thermal behaviour, and information on the disposition of the guests within the interlayer region have been derived. At full intercalation the diamines form a monolayer of extended molecules with their axis inclined at 58° to the plane of the sheet. The terminal amino groups are protonated by the —POH groups of the host, thus each diamine binds adjacent layers and, in a sense, transforms a layered structure into a framework structure that may have an accessible or potentially accessible porosity. The intercalation compound Zr(HOPO₃)₂·0.5NH₂(CH₂)₈NH₂ is indeed able to include polar molecules such as water and short chain alkanols.     

Minimal boundaries enclosing a given volume

We prove some facts concerning surfaces of minimal area bounding regions of prescribed volume in ⁿ. The main result we prove is that the mean curvature of such a surface is constant, if possibly a discontinuous function of the enclosed volume. The boundary behaviour of the solutions is also discussed.     

Adsorption of crude oil on anhydrous and hydrophobized vermiculite

This publication reports the adsorption of crude oil on vermiculite samples, expanded and hydrophobized with carnauba (Copernícia Cerífera) wax. The adsorption studies were performed by using columns filled with the vermiculite matrices and by dispersion of the vermiculite samples in an oil-water (50 ppm of oil) emulsion. The hydrate vermiculite exhibits a very low adsorption capacity against crude oil. On the other hand, anhydrous (expanded) and hydrophobized matrices show a high adsorption capacity. The 10% hydrophobized matrix show a 50% increased adsorption capacity, in comparison with the expanded one. For adsorption performed in the water-oil emulsion, saturation of the solid hydrophobized matrix is achieved after 60 min. The hydrophobized samples exhibit adsorption factors in the 0.7-1.0 range.     

Polyoxometalate Derivatives with Multiple Organic Groups. 2. Synthesis and Structures of Tris(organotin) alpha, beta-Keggin Tungstosilicates

Eight tris(organotin)-substituted Keggin tungstosilicate heteropolyanions have been synthesized and characterized by elemental analysis, infrared and M?ssbauer spectroscopy, multinuclear NMR, and X-ray crystallography. The new anions contain alpha- or beta-SiW(9)O(34)(10)(-) moieties and are of two structural types, [(RSn)(3)(SiW(9)O(37))](7)(-) (R, isomer: Ph, alpha-, 1; n-Bu, alpha-, 2; Ph, beta-, 3; n-Bu, beta-, 4) and [(RSnOH)(3)(SiW(9)O(34))(2)](14)(-) (Ph, alpha-, 5; n-Bu, alpha-, 6; Ph, beta-, 7; n-Bu, beta-, 8). Crystals of Cs(4)H(3)[(PhSn)(3)(SiW(9)O(37))].8H(2)O (anion 3) are monoclinic, space group C2/c, with lattice constants a = 48.91(2) ?, b = 12.111(3) ?, c = 20.334(9) ?, beta = 102.30 degrees, and Z = 8. The anion has nominal C(3)(v)() symmetry and has a structure with three corner-shared WO(6) octahedra of the beta-Keggin anion replaced by three PhSnO(5) groups. Crystals of Cs(9)H(5)[(BuSnOH)(3)(SiW(9)O(34))(2)].36H(2)O (anion 6) are tetragonal, space group P&fourmacr;2(1)m, with lattice constants a = b = 29.005(4) ?, c = 13.412(4) ?, and Z = 4. The anion has the anticipated D(3)(h)() symmetry and contains three BuSnOH groups sandwiched between A,alpha-SiW(9)O(34)(10)(-) anions.     

Symmetries and asymmetries in classical and relativistic electrodynamics

By a comparison between Maxwell's electrodynamics classically interpreted (MT) and relativistic electrodynamics (RED), this paper discusses whether the asymmetries in MT mentioned by A. Einstein in his 1905 relativity paper are only of a conceptual nature or rather involve specific empirical claims. It is shown that in fact MT predicts strongly asymmetric behaviour for very simple interactions, and an analysis is made of the extent of the symmetry achieved by means of relativistic postulates. A low velocity experiment is suggested which could provide another test of the accuracy of RED with respect to MT.     

Fluid-like behavior of a one-dimensional granular gas

We study the properties of a one-dimensional (1D) granular gas consisting of N hard rods on a line of length L (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature Tb and viscosity gamma. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature Tg=mv2, kinetic pressure, and density rho=N/L. Thereafter, we consider the fluctuations around the average behavior obtaining a slightly non-Gaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the k approximately 0 region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical subdiffusive behavior of 1D stochastically driven systems, i.e., approximately Dt(1/2), where D for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave vectors.     

The crystal and molecular structure of a dinuclear copper(II) complex of a Robson-type macrocycle, [Cu2(C26H30N4O2)(H2O)2](BF4)2

Summary The crystal structure of the dinuclear complex [Cu₂(C₂₆H₃₀-N₄O₂)(H₂O)₂](BF₄)₂ was determined by x-ray crystallography. The crystals are triclinic, P¯1, witha = 10.945(5),b = 8.703(5),c = 8.495(5) Å, = 103.86(3)°, = 105.73(3)°, = 85.77(3)°, V = 756 ų D_c = 1.65 g cm^–3 for Z = 1. The copper(II) atoms are 5-coordinate and square-pyramidal. Selected bond distances are: Cu-N, 1.91 Å (mean); Cu-O(base) = 1.90(1) and 1.91(1) Å; Cu-O(apical) = 2.47(1) Å; There are O(water)-H ... F interionic hydrogen bonds in the structure. The Cu .. Cu distance is 2.847 Å.