Multiple Unbounded Positive Solutions for Three-Point BVPs with Sign-Changing Nonlinearities on the Positive Half-Line

This work is concerned with the existence of unbounded positive solutions for a second-order nonlinear three-point boundary value problem on the positive half-line. The interesting points of the results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using recent fixed point theorems on cones in a special Banach space.     

Polynitrile anions as ligands: From magnetic polymeric architectures to spin crossover materials

The use of polynitrile anions as ligands (L) either alone or in combination with neutral co-ligands (L′) is a very promising and appealing strategy to get molecular architectures with different topologies and dimensionalities thanks to their ability to coordinate and bridge metal ions in many different ways. The presence of several potentially coordinating nitrile groups (or even other donor groups as –OH, –SH or –NH₂), their rigidity and their electronic delocalization allow the synthesis of original magnetic high dimensional coordination polymers with transition metals ions. Furthermore, these ligands have shown coordinating and bridging capabilities in novel discrete and polymeric bistable materials (materials showing original magnetic behaviours or spin crossover (SCO) transitions). Here we report an overview of the results obtained with some of these modified polynitrile ligands, showing their rich coordination chemistry and their crucial role in new molecular materials exhibiting unusual magnetic transitions.     

A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository

We prove existence of solutions for a new model of two compressible and partially miscible phase flow in porous media, applied to gas migration in an underground nuclear waste repository. This model, modeling fully and partially water saturated situations, consist of a coupled system of quasilinear parabolic partial differential equations. We seek a new set of variables in order to obtain a system which belongs to the class of equations considered by Alt and Luckhaus such that it would be possible to use their existence theorem. A simulation of a numerical test case is performed in order to numerically demonstrate the ability of this model to take in account the appearance of one phase. To cite this article: F. Smaï, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Positive Solutions for Singular BVPs with Sign Changing and Derivative Depending Nonlinearity on the Positive Half-Line

This work is devoted to the existence of positive, vanishing nontrivial solutions for singular boundary value problems on the half-line. The nonlinearity, which encompasses some physical laws, depends on the solution and its derivative, may exhibit a singularity at the origin in its second argument and is further allowed to change sign. Existence results are proved using two different methods: the upper and lower solutions technique and the fixed point index on cones of weighted Banach spaces. The singularity is treated by means of regularization, approximation and compactness arguments. The problem originates from chemistry and biology.     

Asymmetric azido-copper(II) bridges: ferro- or antiferromagnetic? experimental and theoretical magneto-structural studies

Reaction of NaN(3) with the [Cu(II)(tn)](2+) ion (tn = 1,3-diaminopropane) in basic aqueous solution yields the azido-bridged complex of formula [Cu(2)(tn)(2)(N(3))(4)] (1), which is characterized by X-ray crystallography. The structure of 1 is made up of dinuclear neutral complexes, of formula [Cu(2)(tn)(2)(N(3))(4)], resulting from the assembling of two mononuclear units through two equivalent end-on azide bridges connecting asymmetrically two Cu(tn)(N(3))(2) entities. These dinuclear units are connected through two asymmetric end-to-end N(3) bridges to form a chain of dimers. Magnetic measurements for compound 1 show weak antiferromagnetic exchange interactions between the Cu(II) ions. The magnetic data were modeled using the susceptibility expression derived for an alternating AF S = 1/2 chain. A very satisfactory fit over the whole temperature range was obtained with g = 2.1438(4), J(1) = -3.71(2) cm(-1), and J(2) = -3.10(2) cm(-1) (J(1) and J(2) are the singlet-triplet separations). This magnetic behavior differs from those observed for similar examples which were reported as having alternating ferro- and antiferromagnetic exchange interactions; thus, DFT calculations were done to understand the nature of the magnetic coupling in such asymmetric end-on and end-to-end N(3) bridges. Theoretical results show that the double asymmetric end-on bridges produce antiferromagnetic coupling while the end-to-end ones can present ferro- or antiferromagnetic coupling depending on the copper coordination sphere.     

New magnetic copper(II) coordination polymers with the polynitrile ligand (C[C(CN)2]3)2- and N-donor co-ligands

Reactions between CuCl2 and K2tcpd (tcpd2- = [C10N6]2- = (C[C(CN)2]3)2-) in the presence of neutral co-ligands (bpym = 2,2'-bipyrimidine, and tn = 1,3-diaminopropane) in aqueous solution yield the new compounds [Cu2(bpym)(tcpd)2(H2O)4] x 2H2O (1), [Cu(tn)(tcpd)] (2), and [Cu(tn)2(tcpd)] x H2O (3), which are characterized by X-ray crystallography and magnetic measurements. Compound 1 displays a one-dimensional structure in which the bpym ligand, acting with a bis-chelating coordination mode, leads to [Cu2(bpym)]4+ dinuclear units which are connected by two mu2-tcpd2- bridging ligands. Compound 2 consists of a three-dimensional structure generated by [Cu(tn)]2+ units connected by a mu4-tcpd2- ligand. The structure of 3 is made up of centrosymmetric planar [Cu(tn)]2+ units connected by a mu2-tcpd2- ligand leading to infinite zigzag chains. In compounds 1 and 3, the bridging coordination mode of the tcpd2- unit involves only two nitrogen atoms of one C(CN)2 wing, while in 2, this ligand acts via four nitrogen atoms of two C(CN)2 wings. Despite this difference, the structural features of the tcpd2- units in 1-3 are essentially similar. Magnetic measurements for compound 1 exhibit a maximum in the chi(m) vs T plot (at approximately 150 K) which is characteristic of strong antiferromagnetic exchange interactions between the Cu(II) metal ions dominated by the magnetic exchange through the bis-chelating bpym. The fit of the magnetic data to a dimer model gives J and g values of -90.0 cm(-1) and 2.12, respectively. For compounds 2 and 3 the thermal variations of the magnetic susceptibility show weak antiferromagnetic interactions between the Cu(II) metal ions that can be well reproduced with an antiferromagnetic regular S = 1/2 chain model that gives J values of -0.07(2) and -0.18(1) cm(-1) with g values of 2.12(1) and 2.13(1) for compounds 2 and 3, respectively (the Hamiltonian is written in all the cases as H = -2JS(a)S(b)).     

Existence Results for Singular Boundary Value Problems on Unbounded Domains in Banach Spaces

In this paper, the Krasnosels’kii fixed point theorem in cones for strict set-contractions is used to investigate the existence of single and twin positive solutions for a class of a two-point boundary value problem of second-order nonlinear differential equations posed on an infinite interval. The nonlinearity, which may have a time-singularity, takes values in a general Banach space and has at most polynomial growth with respect to the unknown.     

Surface functionalization of two-photon dye-doped mesoporous silica nanoparticles with folic acid: cytotoxicity studies with HeLa and MCF-7 cancer cells

Two-photon dye-doped mesoporous silica nanoparticles (NPs) have been conjugated with folic acid (FA) in order to obtain efficient nanotools for bioimaging of cancer cells. The surface of the NPs was first functionalized with 3-aminopropyltriethoxysilane. The amine-covered NPs were subsequently reacted with an activated ester derivative of FA. Cytotoxicity studies performed with MCF7 and HeLa cancer cells demonstrate that these functionalized NPs are much less cytotoxic than the non-functionalized NPs against both cell lines. Unfortunately, the grafting of FA enables the formation of charge transfer complexes between the two-photon dye and FA which leads to quenching of the fluorescence of the NPs. Hence although these NPs cannot be used for biomaging purposes, they offer interesting potentialities if the two-photon dye used can be replaced by a two-photon fluorophore which do not interact with FA or if the interaction between the encapsulated dye and FA can be prevented by using a suitable spacer between the surface and the FA moiety.     

Study of cesium phospho(vanado)molybdates active in the oxidative dehydrogenation of cyclohexane

Cs₂.₅M_0.08H_0.26PMo₁₂O₄₀and Cs₂.₅M_0.08H_1.26PMo₁₁VO₄₀(M: Ni, Fe) heteopolyanions were selectively prepared, characterized by IR, Raman, ³¹P NMR, XPS and XRD and tested in the ODH of cyclohexane. The salt structure, and reaction mechanism and kinetics are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cu(tn)]3[Cr(CN)6](2).3H2O: a unique two-dimensional Cu-Cr cyano-bridged ferromagnet (tn = 1,3-diaminopropane)

Reaction of the two-coordinate 'assembling complex-ligand' [Cu(tn)]2+ with the building block [Cr(CN)6]3- leads to a unique two-dimensional Cu-Cr cyano-bridged ferromagnet with unusual mu 3- and mu 4-bridging [Cu(tn)]2+ units.