Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Nonhomogeneous Cooling, Entropic Gravity and MOND Theory

In this paper, by using the holographic principle, a modified equipartition theorem where we assume that below a critical temperature the energy is not equally divided on all bits, and the Unruh temperature, we derive MOND theory and a modified Friedmann equation compatible with MOND theory. Furthermore, we rederive a modified Newton’s law of gravitation by employing an adequate redefinition of the numbers of bits.     

Histochemistry of skin glands of Trachycephalus aff. venulosus Laurenti, 1768 (Anura, Hylidae)

The skin of the adult tree frog, Trachycephalus aff. venulosus, was investigated by light microscopy. Histochemistry was carried out using various stain techniques and showed the basic integument morphology of the skin with squamous epithelium in the epidermis and connective tissue in the dermis, subdivided into spongy and compact layers. The integument observed contains two types of gland; the mucous glands and granular glands. The mucous glands are small and located in the upper layer of the stratum spongiosum of the connective tissue and contain neutral and acid sulfated glycoproteins. The granular glands are large and form a syncytial secretory compartment within the acinus, which is surrounded by smooth muscle cells. Histochemical analyses demonstrated the presence of collagen proteins in both types of gland. An unusual finding was the different densities of the granules in the granular glands. The morphological characteristics of the integument in Trachycephalus aff. venulosus was also compared with others species of Anura.     

Mixed pseudohalide complexes of copper(II). Crystal and molecular structure of [Cu(N3)(NCS)(tmen)] n and of [Cu(N3)(NCO)(tmen)]2 (tmen = N,N,N′,N′-tetramethylethylenediamine)

The compounds [Cu(N₃)(NSC)(tmen)]_n (1), [Cu(N₃)(NCO)(tmen)]_n (2) and [Cu(N₃)(NCO)(tmen)]₂ (3) (tmen=N,N,N′,N′-tetramethylethylenediamine) were synthesized and studied by i.r. spectroscopy. Single crystals of compounds (1) and (3) were obtained and characterized by X-ray diffraction. The structure of compound (1) consists of neutral chains of copper(II) ions bridged by a single azido ligand showing the asymmetric end-to-end coordination fashion. Each copper ion is also surrounded by the other three nitrogen atoms; two from one N,N,N′,N′-tetramethylethylenediamine and one from a terminal bonded thiocyanate group. Compound (2) decomposes slowly in acetone and the product formed [Cu(N₃)(NCO)(tmen)]₂ (3) crystallizes in the monoclinic system (P2₁). The structure of (3) consists of dimeric units in which the Cu atoms are penta-coordinated and connected by μ(1,3) bridging azido and cyanate ligands. In both cases the five coordinated atoms give rise to a slightly distorted square-based pyramid coordination geometry at each copper ion. The thermal behavior of [Cu(N₃)(NSC)(tmen)]_n (1) and [Cu(N₃)(NCO)(tmen)]_n (2) were investigated and the final decomposition products were identified by X-ray powder diagrams.     

Photoluminescent layered Y(III) and Tb(III) silicates doped with Ce(III)

The synthesis and structural characterization of new layered rare-earth silicates K(3)[M(1-a)Ce(a)Si(3)O(8)(OH)(2)], M = Y(3+), Tb(3+), a < 1 (AV-22 materials), have been reported. These materials combine the properties of layered silicates, such as intercalation chemistry, and photoluminescence and may find applications in new types of sensor devices. For mixed Tb/Ce-AV-22, evidence has been found for the energy transfer from the large Ce(3+) 4f( 1) --> 5d(1) broad band to the sharp Tb(3+) 4f (8) lines. This energy transfer allows the fine-tuning of the color emission in the blue-green region of the chromaticity diagram. Upon Ce(3+) excitation (342 nm), the radiance of Tb/Ce-AV-22 is approximately 2 times higher than that measured under direct Tb(3+) excitation, which reinforces the existence of effective room-temperature Ce(3+)-to-Tb(3+) energy transfer.     

Mono- and dinuclear palladium(II) compounds containing nitrogen ligands. Crystal and molecular structure of [Pd(N,C-dmba)(NCO)(2,3-lut)] and [Pd(H2CCOMe)Cl(2,2′-bipy)]

The cyanate-bridged cyclopalladated compound [Pd(N,C-dmba)(-NCO)]₂ (1)(dmba = PhCH₂NMe₂) reacts in CH₂Cl₂ with 2,3-lutidine (2,3-lut), 3,4-lutidine (3,4-lut), 2,2-bipyridine (2,2-bipy) and 4,4-bipyridine (4,4-bipy), to give [Pd(N,C-dmba)(NCO)(2,3-lut)](2), [Pd(N,C-dmba)(NCO)(3,4-lut)](3), [{Pd(N,C-dmba)(NCO)}₂(-2,2-bipy)]· CH₂Cl₂ (4) and [{Pd(N,C-dmba)(NCO)}₂(-4,4-bipy)]· CH₂Cl₂ (5), respectively. The compounds were characterized by elemental analysis, i.r. and n.m.r. spectroscopy and also by t.g.a. The i.r. spectra of (2–5) display typical bands of monodentate N-bonded cyanate groups, whereas the n.m.r. data of (4) are consistent with the presence of a bridging 2,2-bipyridine ligand. Complex (4) decomposes slowly in acetone. One of the products formed, [Pd(H₂CCOMe)Cl(2,2-bipy)](6), was characterized by X-ray diffraction. As inferred from the t.g.a., the thermal stability decreases in the order:[{Pd(N,C-dmba)(NCO)}₂(-4,4-bipy)].CH₂Cl₂ (5) > [Pd(N,C-dmba)(2,3-lut)(NCO)](2)=[Pd(N,C-dmba)(3,4-lut)(NCO)](3) > [{Pd(N,C-dmba)(NCO)}₂(-2,2-bipy)]· CH₂Cl₂ (4). According to thermal analysis and X-ray diffraction patterns compounds (2–3) decompose into metallic palladium Pd(0), whereas (4–5) decompose with the formation of PdO. The X-ray crystal and molecular structure of [Pd(N,C-dmba)(NCO)(2,3-lut)](2) was determined. The lutidine unit is perpendicular to the coordination plane.