Generalized inverses and the maximal radius of regularity of a Fredholm operator

Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operatorT is computed in terms of the spectral radius of a generalized inverse ofT. This provides a partial answer to a conjecture of J. Zemánek.     

Influence of chlorine substitution on the self-assembly of zinc phthalocyanine

The adsorption and ordering of zinc phthalocyanine (ZnPc) and octachloro zinc phthalocyanine (ZnPcCl(8)) on an Ag(111) surface is studied in situ by scanning tunneling microscopy under ultrahigh vacuum. Two-dimensional self-assembled supramolecular domains are observed for these two molecules. We show how substituting chlorine atoms for half of the peripheral hydrogen atoms on ZnPc influences the self-assembly mechanisms. While intermolecular interactions are dominated by van der Waals forces in ZnPc molecular networks, ZnPcCl(8) molecular packing undergoes a sequential phase evolution driven by the creation of C-Cl...H-C hydrogen bonds between adjacent molecules. At the end of this evolution, the final molecular assembly involves all possible hydrogen bonds. Our study also reveals the influence of molecule-substrate interactions through the presence of fault lines generating a stripe structure in the molecular film.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

Circularly polarized x rays: another probe of ultrafast molecular decay dynamics

Dissociative nuclear motion in core-excited molecular states leads to a splitting of the fragment Auger lines: the Auger-Doppler effect. We present here for the first time experimental evidence for an Auger-Doppler effect following F1s → a(1g)* inner-shell excitation by circularly polarized x rays in SF(6). In spite of a uniform distribution of the dissociating S-F bonds near the polarization plane of the light, the intersection between the subpopulation of molecules selected by the core excitation with the cone of dissociation induces a strong anisotropy in the distribution of the S-F bonds that contributes to the scattering profile measured in the polarization plane.     

Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System

We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of the smaller of the three bodies. The three heavy bodies are assumed to move in a plane under their mutual gravity, and the fourth body to move in the three-dimensional space under the gravitational influence of the three heavy bodies, but without affecting them. We first find that the triangular central configuration of the three heavy oblate bodies is a scalene triangle (rather than an equilateral triangle as in the point mass case). Then, assuming that these three bodies are in such a central configuration, we perform a Hill approximation of the equations of motion describing the dynamics of the infinitesimal body in a neighborhood of the smaller body. Through the use of Hill’s variables and a limiting procedure, this approximation amounts to sending the two larger bodies to infinity. Finally, for the Hill approximation, we find the equilibrium points for the motion of the infinitesimal body and determine their stability. As a motivating example, we identify the three heavy bodies with the Sun, Jupiter, and the Jupiter’s Trojan asteroid Hektor, which are assumed to move in a triangular central configuration. Then, we consider the dynamics of Hektor’s moonlet Skamandrios.

     

Amine oxidase amperometric biosensor coupled to liquid chromatography for biogenic amines determination

A selective and sensitive method is presented for biogenic amines (BA) determination. The novelty consists in coupling a highly selective electrochemical biosensor to a weak acid cation-exchange column for online detection of amines. A bienzyme design, based on a recently isolated amine oxidase from grass pea and commercial horseradish peroxidase, was used for the biosensor construction. The enzymes were co-immobilized on the surface of a graphite electrode together with the electrochemical mediator (Os-redox polymer). The electrochemical detection was performed at a low applied potential (?50 mV vs. Ag/AgCl, KCl_0.1 M), where biases from interferences are minimal. The separation and determination of six BA, with relevance in food analysis (tyramine, putrescine, cadaverine, histamine, agmatine and spermidine), were investigated. Irrespective of the BA nature, the amine oxidase-based biosensor showed a linear response up to 5 mM, and its sensitivity decreases in the following order: cadaverine, putrescine, spermidine, agmatine, histamine and tyramine. The approach was used to estimate the BA content in fish samples, after their extraction with methanesulfonic acid.     

A 2D coordination polymer with canted ferromagnetism constructed from ferromagnetic [Ni(II)Co(II)] nodes

A bimetallic coordination polymer, infinity (2)[{LNi (II)Co (II)}(dca) 2], has been constructed from heterobinuclear [Ni (II)Co (II)] nodes and dicyanamido spacers [L (2-) is the dianion of the Schiff base resulting from the 2:1 condensation of 3-methoxysalicyladehyde with 1,3-propanediamine; L (2-) = N, N'-propylenebis(3-methoxysalycilideneiminato)]. The intranode Co (II)-Ni (II) interaction was found to be ferromagnetic because of the orthogonality of the magnetic orbitals. Below 12 K, the onset of the canted ferromagnetic ordering is observed.     

Detection of negative molecular ions in acrylic acid plasma: some implications for polymerization mechanisms

There is much scientific and commercial interest in plasma polymers to modify surface chemistry. To date, only neutral and positively charged species have been detected in the commonly applied acrylic acid plasma. Using time-averaged negative ion mass spectrometry, we demonstrate that large, negatively charged species exist in the plasma, contrary to previous studies that detected only neutral and positive species. We briefly outline how negative molecules may contribute to the deposition of plasma polymer in the acrylic acid system.     

Finite element approximation of spatially extended predator–prey interactions with the Holling type II functional response

We study the numerical approximation of the solutions of a class of nonlinear reaction–diffusion systems modelling predator–prey interactions, where the local growth of prey is logistic and the predator displays the Holling type II functional response. The fully discrete scheme results from a finite element discretisation in space (with lumped mass) and a semi-implicit discretisation in time. We establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations. Numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions. The class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics, expressed in nondimensional form. The theoretical techniques were adapted from a previous study of an idealised reaction–diffusion system (Garvie and Blowey in Eur J Appl Math 16(5):621–646, 2005).