Abstract:
In the present work, the hybrid catalyst films of TiO_{2}/CuO containing up to 10% in mol of copper were deposited onto glass surface. Precursor solutions were obtained by citrate precursor method. Films were porous and the average particle size was 20 nm determined by FEG-SEM analysis. The photocatalytic activities of these films were studied using Rhodamine B as a target compound in a fixed bed reactor developed in our laboratory and UV lamp. It was observed that the addition of copper to TiO_{2} increased significantly its photocatalytic activity during the oxidation of Rhodamine B. The degradation exceeded 90% within 48 hours of irradiation compared to 38% when pure TiO_{2} was used. Moreover, there was a reduction in the particles band gap energy when compared to that of pure TiO_{2}. These results indicate that the TiO_{2}/CuO films are promising catalysts for the development of fixed bed reactors to be used to treat effluents containing azo dyes.

Abstract:
the compounds 5-nitro-8-quinolinol and 5,7-dinitro-8-quinolinol were obtained by nitration of the chelant 8-quinolinol. the compounds were characterized through ea, mnr, xrd, ir, tg, dta and dsc. it was verified through thermal analysis that the compounds show consecutive processes of sublimation, fusion and vaporization. during the vaporization process, partial thermal decomposition was observed, with formation of carbonaceous residues. considering a slower heating rate, the sublimation is the prevalent process to the nitro-derivatives while the vaporization is the main process to 8-quinolinol. the thermal stability follows the decreasing order from 5,7-dinitro-8-quinolinol to 5-nitro-8-quinolinol to 8-quinolinol.

Abstract:
The compounds 5-nitro-8-quinolinol and 5,7-dinitro-8-quinolinol were obtained by nitration of the chelant 8-quinolinol. The compounds were characterized through EA, MNR, XRD, IR, TG, DTA and DSC. It was verified through thermal analysis that the compounds show consecutive processes of sublimation, fusion and vaporization. During the vaporization process, partial thermal decomposition was observed, with formation of carbonaceous residues. Considering a slower heating rate, the sublimation is the prevalent process to the nitro-derivatives while the vaporization is the main process to 8-quinolinol. The thermal stability follows the decreasing order from 5,7-dinitro-8-quinolinol to 5-nitro-8-quinolinol to 8-quinolinol.

Abstract:
In this paper we establish a variation of the Splitter Theorem. Let $M$ and $N$ be simple 3-connected matroids. We say that $x\in E(M)$ is vertically $N$-contractible if $si(M/x)$ is a 3-connected matroid with an $N$-minor. Whittle (for $k=1,2$) and Costalonga(for $k=3$) proved that, if $r(M)- r(N)\ge k$, then $M$ has a $k$-independent set $I$ of vertically $N$-contractible elements. Costalonga also characterized an obstruction for the existence of such a 4-independent set $I$ in the binary case, provided $r(M)-r(N)\ge 5$, and improved this result when $r(M)-r(N)\ge 6$, and in the graphic case. In this paper we generalize the results of Costalonga to the non-binary case. Moreover, we apply our results to the study of properties similar to 3-roundedness in classes of matroids.

Abstract:
Let $M$ be a 3-connected binary matroid and let $Y(M)$ be the set of elements of $M$ avoiding at least $r(M)+1$ non-separating cocircuits of $M$. Lemos proved that $M$ is non-graphic if and only if $Y(M)\neq\emp$. We generalize this result when by establishing that $Y(M)$ is very large when $M$ is non-graphic and $M$ has no $M\s(K_{3,3}"')$-minor if $M$ is regular. More precisely that $|E(M)-Y(M)|\le 1$ in this case. We conjecture that when $M$ is a regular matroid with an $M\s(K_{3,3})$-minor, then $r\s_M(E(M)-Y(M))\le 2$. The proof of such conjecture is reduced to a computational verification.

Abstract:
In this paper we prove two main results about obstruction to graph planarity. One is that, if $G$ is a 3-connected graph with a $K_5$-minor and $T$ is a triangle of $G$, then $G$ has a $K_5$-minor $H$, such that $E(T)\cont E(H)$. Other is that if $G$ is a 3-connected simple non-planar graph not isomorphic to $K_5$ and $e,f\in E(G)$, then $G$ has a minor $H$ such that $e,f\in E(H)$ and, up to isomorphisms, $H$ is one of the four non-isomorphic simple graphs obtained from $K_{3,3}$ by the addiction of \,0, 1 or 2 edges. We generalize this second result to the class of the regular matroids.

Abstract:
A radius-$r$ extend ball with center in an $1$-dimensional vector subspace $V$ of $\mathbb{F}_q^3$ is the set of elements of $\mathbb{F}_q^3$ with Hamming distance to $V$ at most $r$. We define $c(q)$ as the size of a minimum covering of $\mathbb{F}_q^3$ by radius-$1$ extend balls. We define a quower as a piece of a toroidal chessboard that extends the covering range of a tower by the northeast diagonal containing it. Let $\xi_D(n)$ be the size of a minimal covering with quowers of an $n\times n$ toroidal board without a northeast diagonal. In this paper we prove, that, for $q\ge 7$, $c(q)=\xi_D(q-1)+2$. Moreover, our proof exhibits a method to build such covers of $\mathbb{F}_q^3$ from the quower coverings of the board. With this new method, we determine $c(q)$ for the odd values of $q$ and improve both existing bounds for the even case.

Abstract:
Let $G$ be a $3$-connected graph with a $3$-connected (or sufficiently small) simple minor $H$. We establish that $G$ has a forest $F$ with at least $\left\lceil(|G|-|H|+1)/2\right\rceil$ edges such that $G/e$ is $3$-connected with an $H$-minor for each $e\in E(F)$. Moreover, we may pick $F$ with $|G|-|H|$ edges provided $G$ is triangle-free. These results are sharp. Our result generalizes a previous one by Ando et. al., which establishes that a $3$-connected graph $G$ has at least $\left\lceil|G|/2\right\rceil$ contractible edges. As another consequence, each triangle-free $3$-connected graph has an spanning tree of contractible edges. Our results follow from a more general theorem on graph minors, a splitter theorem, which is also established here.

Abstract:
We prove the following splitter theorem for graphs and its generalization for matroids: Let $G$ and $H$ be $3$-connected simple graphs such that $G$ has an $H$-minor and $k:=|V(G)|-|V(H)|\ge 2$. Let $n:=\lfloor(k+3)/2\rfloor$. Then there are sets $X_1,...,X_n\cont E(G)$ such that each $G/X_i$ is a $3$-connected graph with an $H$-minor, each $X_i$ is a singleton set or the edge set of a triangle of $G$ with $3$ degree-$3$ vertices and $X_1\u...\u X_n$ contains no edge sets of circuits of $G$ other than the $X_i$'s. This implies that $G$ has a forest $F$ with at least $(3/5)\lfloor(k+3)/2\rfloor$ edges, with the property that $G/e$ is $3$-connected with an $H$-minor for each $e\in F$. The main result extends previous ones of Whittle (for $k=1,2$) and the Author (for $k=3$).

Abstract:
reported herein are the synthesis and characterization of the hexadentate h2l pro-ligand (n,n',n,n'-bis[(2-hydroxy-3,5-di-tert -butylbenzyl)(2-pyridylmethyl)]ethylenediamine), as a further derivative of the well known pro-ligand h2bbpen which contains two phenolate and two pyridyl pendant arms. the phenolate groups in h2l are suitably protected by bulky substituents (tert-butyl) in the ortho- and para- positions, from which stable phenoxyl radical complexes can be formed. thus, we have synthesized four new mononuclear complexes with mniii, gaiii, iniii and feiii which through electrochemical oxidation generate one- and two-electron oxidized phenoxyl species in solution. these radical species were characterized by uv-vis, electronic paramagnetic resonance and electrochemical studies. as expected, in the case of the gaiii, iniii and feiii complexes no metal-centered oxidation was observed. however, the manganese complex undergoes metal- and ligand-centered oxidation processes and therefore a phenoxyl radical-mniv complex can be generated in solution. the crystal structures of the [mniii(l)]+ and [gaiii(l)]+ complexes were determined by x-ray crystallographic analyses revealing monocationic complexes with distorted octahedral geometries.