A bivariate non-homogeneous birth and death model for predator–prey interactions

We propose a bivariate non-homogeneous birth and death process as a model for predator–prey interactions. Its expectation is periodic, as it is a solution to the classical Lotka–Volterra system. Moreover, the mean age at extinction, as defined in Kendall (1948), is infinite.     

Collision and escape orbits in a generalized Hénon–Heiles model

The motion of a material point of unit mass in a field determined by a generalized Hénon–Heiles potential $U=A{q}_1^2+B{q}_2^2+C{q}_1^2{q}_2+D{q}_2^3$, with $(q_1,q_2)=$ standard Cartesian coordinates and $(A,B,C,D)\in {(0,\infty )}^2\times R^2$, is addressed for two limit situations: collision and escape. Using McGehee-type transformations, the corresponding collision and infinity boundary manifolds pasted on the phase space are determined. These are fictitious manifolds, but, due to the continuity with respect to initial data, their flow determines the near by orbit behaviour.The dynamics on the collision and infinity manifolds is fully described. The topology of the flow on the collision manifold is independent of the parameters. In the full phase space, while spiraling collision orbits are present, most of the orbits avoid collision. The topology of the flow on the infinity manifold changes as the ratio between $C$ and $D$ varies. More precisely, there are two symmetric pitchfork bifurcations along the line $2C?3D=0$, due to the reshaping of the potential along the bifurcation line. Besides rectilinear and spiraling orbits, the near-escape dynamics includes oscillatory orbits, for which angular momentum alternates sign.     

Dinuclear amine-thiophenolate complexes coligated by ferrocenemonocarboxylate and 1,1'-ferrocenedicarboxylate anions: preparation, characterization and structures of trinuclear [LMII 2(O2CC5H4FeCp)]+ and Pentanuclear [(LMII 2)2(O2CC5H4)2Fe]2+ complexes (M=Co, Ni, Zn)

A series of novel tri- and pentanuclear complexes composed of dinuclear LM(2) units (M=Co, Ni, Zn; L=24-membered macrocyclic hexaazadithiophenolate ligand) and ferrocenecarboxylate ([CpFeC(5)H(4)CO(2)](-)) or 1,1'-ferrocenedicarboxylate ([Fe(C(5)H(4)CO(2))(2)](2-)) groups is reported. The complexes [LM(II) (2)(O(2)CC(5)H(4)FeCp)](+) (M=Co (6), Ni (7), Zn (8)) and [(LM(II) (2))(2)(O(2)CC(5)H(4))(2)Fe](2+) (M=Co (9), Ni (10)) have been prepared by substitution reactions from labile [LM(II) (2)L'](+) precursors (L'=Cl, OAc) and the respective ferrocenecarboxylate anions in methanol. Mixed-valent [(LCo(II)Co(III))(2)(O(2)CC(5)H(4))(2)Fe](4+) (11) was prepared by oxidation of 9 with bromine. Complexes 7[BPh(4)], 8[BPh(4)], 9[BPh(4)](2), 10[BPh(4)](2), and 11[ClO(4)](4) have been characterized by X-ray crystallography; showing that the ferrocenyl carboxylates act as bidentate (7, 8) or bis-bidentate (9-11) bridging ligands towards one or two bioctahedral LM(2) subunits, respectively. The structures are retained in solution as indicated by NMR spectroscopic studies on the diamagnetic Zn(2)Fe complex 8[ClO(4)]. Electrochemical studies reveal significant anodic potential shifts for the oxidation potential of the ferrocenyl moieties upon complexation and the magnitude of the potential shift appears to correlate with the charge of the LM(2) subunits. This is qualitatively explained in terms of destabilizing electrostatic (Coulomb) interactions between the M(2+) ions of the LM(2) unit and the proximate ferrocenium fragment. An analysis of the temperature-dependent magnetic susceptibility data for 10[BPh(4)](2) shows the presence of weak ferromagnetic magnetic exchange interactions between the Ni(II) ions in the LNi(2) units. The exchange coupling across the ferrocenedicarboxylate bridge is negligible.     

Complexation of phenolic guests by endo- and exo-hydrogen-bonded receptors

This article describes the complexation of phenol derivatives by hydrogen-bonded receptors. These phenol receptors are formed by self-assembly of calix[4]arene dimelamine or tetramelamine derivatives with 5,5-diethylbarbiturate (DEB) or cyanurate derivatives (CYA). The double rosette assemblies 3(3).(DEB)6/(CYA)6 have their phenol-binding functionalities (ureido groups) at the top and at the bottom of the double rosette (exo-receptors). The tetrarosette assemblies 4(3).(DEB)12/(CYA)12 form a cavity with binding sites between the two double rosettes for guest encapsulation (endo-receptors). An intrinsic binding constant Ka of 202 M-1 and 286 M-1 for the binding of 4-nitrophenol to the ureido functionalized exo- and endo-receptors, respectively, was observed. For the exo-receptor a 1:6 stoichiometry was observed while for the endo-receptor 1:4 binding stoichiometry was determined by Job plot and MALDI-TOF MS. The important role that the hydroxy group's acidity plays in the complexation of 4-nitrophenol is clarified by binding studies with different phenol derivatives. The hydrogen-bonded receptors showed a much smaller response towards less acidic phenol derivatives.     

A Class of Integrable Flows on the Space of Symmetric Matrices

For a given skew symmetric real n × n matrix N, the bracket [X, Y] _N = XNY − YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n × n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to investigate the geometry, integrability, and linearizability of the Hamiltonian system , or equivalently in Lax form, the equation on this space along with a detailed study of the Poisson geometry itself. If N has distinct eigenvalues, it is proved that this system is integrable on a generic symplectic leaf of the Lie-Poisson structure of Sym(n, N). This is established by finding another compatible Poisson structure. If N is invertible, several remarkable identifications can be implemented. First, (Sym(n, N), [·, ·]) is Lie algebra isomorphic with the symplectic Lie algebra associated to the symplectic form on given by N ⁻¹. In this case, the system is the reduction of the geodesic flow of the left invariant Frobenius metric on the underlying symplectic group Sp(n, N ⁻¹). Second, the trace of the product of matrices defines a non-invariant non-degenerate inner product on Sym(n, N) which identifies it with its dual. Therefore Sym(n, N) carries a natural Lie-Poisson structure as well as a compatible “frozen bracket” structure. The Poisson diffeomorphism from Sym(n, N) to maps our system to a Mischenko-Fomenko system, thereby providing another proof of its integrability if N is invertible with distinct eigenvalues. Third, there is a second ad-invariant inner product on Sym(n, N); using it to identify Sym(n, N) with itself and composing it with the dual of the Lie algebra isomorphism with , our system becomes a Mischenko- Fomenko system directly on Sym(n, N). If N is invertible and has distinct eigenvalues, it is shown that this geodesic flow on Sym(n, N) is linearized on the Prym subvariety of the Jacobian of the spectral curve associated to a Lax pair formulation with parameter of the system. If, on the other hand, N has nullity one and distinct eigenvalues, in spite of the fact that the system is completely integrable, it is shown that the flow does not linearize on the Jacobian of the spectral curve. Research partially supported by NSF grants CMS-0408542 and DMS-0604307. Research partially supported by the Swiss SCOPES grant IB7320-110721/1, 2005-2008, and MEdC Contract 2-CEx 06-11-22/25.07.2006. Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. Research partially supported by the Swiss NSF and the Swiss SCOPES grant IB7320-110721/1.     

Polylactic acid (PLA)/Silver-NP/VitaminE bionanocomposite electrospun nanofibers with antibacterial and antioxidant activity

The antibacterial property of silver nanoparticles (Ag-NPs) and the antioxidant activity of Vitamin E have been combined by incorporation of these two active components within polylactic acid (PLA) nanofibers via electrospinning (PLA/Ag-NP/VitaminE nanofibers). The morphological and structural characterizations of PLA/Ag-NP/VitaminE nanofibers were performed by Scanning Electron Microscopy (SEM), Transmission Electron Microscopy and X-ray diffraction. The average fiber diameter was 140 ± 60 nm, and the size of the Ag-NP was 2.7 ± 1.5 nm. PLA/Ag-NP/VitaminE nanofibers inhibited growth of Escherichia coli, Listeria monocytogenes and Salmonella typhymurium up to 100 %. The amount of released Ag ions from the nanofibers immersed in aqueous solution was determined by Inductively Coupled Plasma Mass Spectrometry, and it has been observed that the release of Ag ions was kept approximately constant after 10 days of immersion. The antioxidant activity of PLA/Ag-NP/VitaminE nanofibers was evaluated according to DPPH (2,2-diphenyl-1-picrylhydrazyl) method and determined as 94 %. The results of the tests on fresh apple and apple juice indicated that the PLA/Ag/VitaminE nanofiber membrane actively reduced the polyphenol oxidase activity. The multifunctional electrospun PLA nanofibers incorporating Ag-NP and Vitamin E may be quite applicable in food packaging due to the extremely large surface area of nanofibers along with antibacterial and antioxidant activities. These materials could find application in food industry as a potential preservative packaging for fruits and juices.     

Heterogeneous gold catalysts for efficient access to functionalized lactones

A novel class of heterogeneous gold catalysts supported on zeolite beta-NH4+ was prepared by the deposition-precipitation method. This new class of catalyst showed interesting catalytic activities for the intramolecular cycloisomerization of gamma-acetylenic carboxylic acids leading to functionalized gamma-alkylidene gamma-butyrolactones. Analysis of the supported gold species with in situ X-ray photoelectron spectroscopy (in situ XPS) suggests that cationic Au (possibly AuIII) can play an important role in such reactions. The high discrepancy in catalyst stability in favor of the Au supported on the zeolite system over bulk Au2O3 is explained by 1) the size of the particles and 2) the reversibility of the redox deactivating process (AuIII-->AuI) in the presence of oxygen for the supported system. The efficiency of this system allowed reaction under mild heterogeneous conditions. The potential for catalyst recycling was also highlighted.     

Thermal behavior of some new triazole derivative complexes

A series of new complexes with mixed ligands of the type [ML(C₃H₃O₂)₂]·nH₂O (((1) M=Mn, n=1; (2) M=Co(II), n=2; (3) M=Ni(II), n=4; (4) M=Cu(II), n=1.5; (5) M=Zn(II), n=0; L=3-amino-1,2,4-triazole and (C₃H₃O₂)=acrylate anion) were synthesized and characterised by chemical analysis and IR data. In all complexes the 3-amino-1,2,4-triazole acts as bridge while the acrylate acts as bidentate ligand except for complex (5) where it is found as unidentate. The thermal behaviour steps were investigated in nitrogen flow. The thermal transformations are complex processes according to TG and DTG curves including dehydration, acrylate ion and 3-amino-1,2,4-triazole degradation respectively. The final products of decomposition are the most stable metal oxides, except for complex (4) that leads to metallic copper.     

Binary volume phase masks in photo-thermo-refractive glass

Permanent binary phase masks with planar surfaces and high tolerance to laser radiation are recorded in the volume of photo-thermo-refractive glass using the contact copying technique and binary amplitude master masks. Conversion of a Gaussian beam to higher order modes is shown.