Composition Operators and Classical Function Theory

(1) The section Linear Fractional Prologue is a context, to be consulted as needed , on the basic properties and classi�cation of linear fractional transformations. Linear fractional maps play a vital role in my work, both as agents for changing coordinates and transforming settings. (2) In the section Fourier series, I discuss how to construct a inner product from given Fourier series , the Dirichlet Kernel and its properties. Then I give the proof of Plancharal theorem and Parseval's theorem which play a good role through out my project. (3) This Littlewood's Theorem section is most important part of my work. After developing some of the basic properties of H2, here we shows that every composition operator acts boundedly on the Hilbert space. As pointed out above, this is essentially Littlewood's Subordination Principle. I present Littlewood's original proof - a beautiful argument that is perfectly transparent in its beauty, but utterly ba�ing in its lack of geometric insight. Much of conclusion can be regarded as an e�ort to understand the geometric underpinning of this theorem. (4) Having established that every composition operator is bounded on H2, we turn to the most natural follow-up question: "Which composition operators are compact?" The Chapter Compact- ness:Introduction sets out the motivation for this problem. The property of "boundedness" for composition operators means that each one takes bounded subsets of H2 to bounded subsets. The question above asks us to specify precisely how much the inducing map � has to compress the unit disc into itself in order to insure that the operator C� compresses bounded subsets of H2 into relatively compact ones. (5) In Chapter Compactness and Univalence we discover that the geometric soul of Littlewood's Theorem is bound up in the Schwarz Lemma. Armed with this insight, we are able to characterize the univalently induced compact composition operators, obtaining a compactness criterion that leads directly to the Julia-Caratheodory Theorem on the angular derivative. (6) In Chapter The Angular Derivative, I give the idea of the proof of Julia-Caratheodory Theorem in a way that emphasizes its geometric content, especially its connection with the Schwarz Lemma

Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay

A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution occurs for each point of such interval. The orbital stability of such bifurcating periodic solution at the extreme points of the interval is ascertained. Lastly global bifurcation aspect of such periodic solutions is studied. The results are illustrated by numerical simulations

Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented

Effect of argon ion energy on the performance of silicon nitridemultilayer permeation barriers grown by hot-wire CVD on polymers

One of the authors (S.M.) acknowledges Direction des Relations Extérieures of Ecole Polytechnique for financial support.Permeation barriers for organic electronic devices on polymer flexible substrates were realized by combining stacked silicon nitride (SiNx) single layers (50 nm thick) deposited by hot-wire chemical vapor deposition process at low-temperature (~100°C) with a specific argon plasma treatment between two successive layers. Several plasma parameters (RF power density, pressure, treatment duration) as well as the number of single layers have been explored in order to improve the quality of permeation barriers deposited on polyethylene terephthalate. In this work, maximumion energy was highlighted as the crucial parameter making it possible to minimize water vapor transmission rate (WVTR), as determined by the electrical calcium test method, all the other parameters being kept fixed. Thus fixing the plasma treatment duration at 8 min for a stack of two SiNx single layers, a minimum WVTR of 5 × 10−4 g/(m2 day), measured at room temperature, was found for a maximum ion energy of ~30 eV. This minimum WVTR value was reduced to 7 × 10−5 g/(m2 day) for a stack of five SiNx single layers. The reduction in the permeability is interpreted as due to the rearrangement of atoms at the interfaces when average transferred ion energy to target atoms exceeds threshold displacement energy.The authors are grateful to Dr. R. Cortes (PMC, Ecole Polytechnique) for XRR analysis, to Dr. P. Chapon (HORIBA Jobin Yvon) for GD-OES analysis and Dr. J. Leroy (CEA Saclay) for XPS analysis. This work was partly supported by the PICS (FrenchPortuguese) project No. 5336. One of the authors (S.M.) acknowledges Direction des Relations Extérieures of Ecole Polytechnique for financial support

The effect of argon plasma treatment on the permeation barrier properties of silicon nitride layers

In this work we produce and study silicon nitride (SiNx) thin films deposited by Hot Wire Chemical Vapor Depo- sition (HW-CVD) to be used as encapsulation barriers for flexible organic photovoltaic cells fabricated on poly- ethylene terephthalate (PET) substrates in order to increase their shelf lifetime. We report on the results of SiNx double-layers and on the equivalent double-layer stack where an Ar-plasma surface treatment was performed on the first SiNx layer. The Ar-plasma treatment may under certain conditions influences the structure of the interface between the two subsequent layers and thus the barrier properties of the whole system. We focus our attention on the effect of plasma treatment time on the final barrier properties. We assess the encapsulation barrier properties of these layers, using the calcium degradation test where changes in the electrical conductance of encapsulated Ca sensors are monitored with time. The water vapor transmission rate (WVTR) is found to be ~3 × 10−3 g/m2·day for stacked SiNx double-layer with 8 min Ar plasma surface treatment.FCT - CNRS PICS (French–Portuguese no: 5336) projectDirection des Relations Extérieures, Ecole Polytechniqu

SU(6), Triquark states, and the pentaquark

The purported observation of a state $\Theta^+$ with strangeness S = +1 led to its quark model interpretation in terms of a pentaquark combination involving a triquark-diquark structure -- the Karliner-Lipkin model. In this work, the proper colour-spin symmetry properties for the $q q \bar{q}$ triquark are elucidated by calculating the SU(6) unitary scalar factors and Racah coefficients. Using these results, the colour-spin hyperfine interactions, including flavour symmetry breaking therein, become straight-forward to incorporate and the pentaquark masses are readily obtained. We examine the effect on the pentaquark mass of (a) deviations from the flavour symmetric limit and (b) different strengths of the doublet and triplet hyperfine interactions. Reference values of these parameters yield a $\Theta^+$ mass prediction of 1601 MeV but it can comfortably accommodate 1540 MeV for alternate choices. In the same framework, other pentaquark states $\Xi$ (S=--2) and $\Theta^c$ (with charm C=--1) are expected at 1783 MeV and 2757 MeV, respectively.Comment: 17 pages, 1 figure. accepted for publication in Phys. Rev.

Synthesis of (Hetero)Macrocycles under Environmentally Friendly Conditions

This work was supported in part by the Russian Science Foundation (References Nos. 18-13-00365 and 18-73-00301)

Low-voltage 2D materials-based printed field-effect transistors for integrated digital and analog electronics on paper

Paper is the ideal substrate for the development of flexible and environmentally sustainable ubiquitous electronic systems, which, combined with two-dimensional materials, could be exploited in many Internet-of-Things applications, ranging from wearable electronics to smart packaging. Here we report high-performance MoS2 field-effect transistors on paper fabricated with a “channel array” approach, combining the advantages of two large-area techniques: chemical vapor deposition and inkjet-printing. The first allows the pre-deposition of a pattern of MoS2; the second, the printing of dielectric layers, contacts, and connections to complete transistors and circuits fabrication. Average ION/IOFF of 8 × 103 (up to 5 × 104) and mobility of 5.5 cm2 V−1 s−1 (up to 26 cm2 V−1 s−1) are obtained. Fully functional integrated circuits of digital and analog building blocks, such as logic gates and current mirrors, are demonstrated, highlighting the potential of this approach for ubiquitous electronics on paper

Indium oxide and copper oxide nanoparticles: efficient catalysts in various organic syntheses

The authors acknowledge the Russian Science Foundation (Ref. # 16-43-02020) for funding

Substrates of the \u3cem\u3eArabidopsis thaliana\u3c/em\u3e Protein Isoaspartyl Methyltransferase 1 Identified Using Phage Display and Biopanning

The role of protein isoaspartyl methyltransferase (PIMT) in repairing a wide assortment of damaged proteins in a host of organisms has been inferred from the affinity of the enzyme for isoaspartyl residues in a plethora of amino acid contexts. The identification of PIMT target proteins in plant seeds, where the enzyme is highly active and proteome long-lived, has been hindered by large amounts of isoaspartate-containing storage proteins. Mature seed phage display libraries circumvented this problem. Inclusion of the PIMT co-substrate, S-adenosylmethionine (AdoMet), during panning permitted PIMT to retain aged phage in greater numbers than controls lacking co-substrate or when PIMT protein binding was poisoned with S-adenosyl homocysteine. After four rounds, phage titer plateaued in AdoMet-containing pans, whereas titer declined in both controls. This strategy identified 17 in-frame PIMT target proteins, including a cupin-family protein similar to those identified previously using on-blot methylation. All recovered phage had at least one susceptible Asp or Asn residue. Five targets were recovered independently. Two in-frame targets were produced in Escherichia coli as recombinant proteins and shown by on-blot methylation to acquire isoAsp, becoming a PIMT target. Both gained isoAsp rapidly in solution upon thermal insult. Mutant analysis of plants deficient in any of three in-frame PIMT targets resulted in demonstrable phenotypes. An over-representation of clones encoding proteins involved in protein production suggests that the translational apparatus comprises a subgroup for which PIMT-mediated repair is vital for orthodox seed longevity. Impaired PIMT activity would hinder protein function in these targets, possibly resulting in poor seed performance