Unitary Representations of Unitary Groups

In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group \U(\cH) of a real, complex or quaternionic separable Hilbert space and the subgroup \U_\infty(\cH), consisting of those unitary operators $g$ for which g - \1 is compact. The Kirillov--Olshanski theorem on the continuous unitary representations of the identity component \U_\infty(\cH)_0 asserts that they are direct sums of irreducible ones which can be realized in finite tensor products of a suitable complex Hilbert space. This is proved and generalized to inseparable spaces. These results are carried over to the full unitary group by Pickrell's Theorem, asserting that the separable unitary representations of \U(\cH), for a separable Hilbert space \cH, are uniquely determined by their restriction to \U_\infty(\cH)_0. For the $10$ classical infinite rank symmetric pairs $(G,K)$ of non-unitary type, such as (\GL(\cH),\U(\cH)), we also show that all separable unitary representations are trivial.Comment: 42 page

Mycobacterium tuberculosis Lipolytic Enzymes as Potential Biomarkers for the Diagnosis of Active Tuberculosis

BACKGROUND: New diagnosis tests are urgently needed to address the global tuberculosis (TB) burden and to improve control programs especially in resource-limited settings. An effective in vitro diagnostic of TB based on serological methods would be regarded as an attractive progress because immunoassays are simple, rapid, inexpensive, and may offer the possibility to detect cases missed by standard sputum smear microscopy. However, currently available serology tests for TB are highly variable in sensitivity and specificity. Lipolytic enzymes have recently emerged as key factors in lipid metabolization during dormancy and/or exit of the non-replicating growth phase, a prerequisite step of TB reactivation. The focus of this study was to analyze and compare the potential of four Mycobacterium tuberculosis lipolytic enzymes (LipY, Rv0183, Rv1984c and Rv3452) as new markers in the serodiagnosis of active TB. METHODS: Recombinant proteins were produced and used in optimized ELISA aimed to detect IgG and IgM serum antibodies against the four lipolytic enzymes. The capacity of the assays to identify infection was evaluated in patients with either active TB or latent TB and compared with two distinct control groups consisting of BCG-vaccinated blood donors and hospitalized non-TB individuals. RESULTS: A robust humoral response was detected in patients with active TB whereas antibodies against lipolytic enzymes were infrequently detected in either uninfected groups or in subjects with latent infection. High specifity levels, ranging from 93.9% to 97.5%, were obtained for all four antigens with sensitivity values ranging from 73.4% to 90.5%, with Rv3452 displaying the highest performances. Patients with active TB usually exhibited strong IgG responses but poor IgM responses. CONCLUSION: These results clearly indicate that the lipolytic enzymes tested are strongly immunogenic allowing to distinguish active from latent TB infections. They appear as potent biomarkers providing high sensitivity and specificity levels for the immunodiagnosis of active TB

A new measurement of direct CP violation in two pion decays of the neutral kaon

The NA48 experiment at CERN has performed a new measurement of direct CP violation, based on data taken in 1997 by simultaneously collecting KL and KS decays into pi0 pi0 and pi+ pi-. The result for the CP violating parameter Re(epsilon'/epsilon) is (18.5 +- 4.5(stat.) +- 5.8(syst.)) x 10^-4

Measurement of the radiative Ke3 branching ratio

We present a measurement of the relative branching ratio of the decay K0 → π± e± νγ (Ke3γ) with respect to K0 → π± e± ν (Ke3 + Ke3γ ) decay. The result is based on observation of 19 000 Ke3γ and 5.6 × 10^6 Ke3 decays. The value of the branching ratio is BR(K0e3γ , E∗γ > 30 MeV, θ∗eγ > 20◦)/ Br(K0e3 ) = (0.964 ± 0.008+0.011-0.009)%. This result agrees with theoretical predictions but is at variance with a recently published result

Measurement of K0e3 form factors

The semileptonic decay of the neutral K meson, K0L → π± e∓ ν (Ke3 ), was used to study the strangeness-changing weak interaction of hadrons. A sample of 5.6 million reconstructed events recorded by the NA48 experiment was used to measure the Dalitz plot density. Admitting all possible Lorentz-covariant couplings, the form factors for vector (f+(q2)), scalar (fS) and tensor (fT) interactions were measured. The linear slope of the vector form factor λ+ = 0.0284 ± 0.0007 ± 0.0013 and values for the ratios |fS/f+(0)| = 0.015 +0.007-0.010 ± 0.012 and |fT/f+(0)| = 0.05 +0.03-0.04 ± 0.03 were obtained. The values for fS and fT are consistent with zero. Assuming only vector–axial-vector couplings, λ+ = 0.0288 ± 0.0004 ± 0.0011 and a good fit consistent with pure V–A couplings were obtained. Alternatively, a fit to a dipole form factor yields a pole mass of M = 859 ± 18 MeV, consistent with the K∗(892) mass

Investigation of K(L,S) -> pi+ pi- e+ e- decays

The KL → π+ π− e+ e− and KS → π+ π− e+ e− decay modes have been studied in detail using the NA48 detector at the CERN SPS. Based on the data collected during the 1998 and 1999 run periods, a sample of 1162 KL → π+ π− e+ e− candidates has been observed with an expected background level of 36.9 events, yielding the branching ratio measurement BR(KL → π+ π− e+ e−) = (3.08 ± 0.20) × 10^−7 . The distribution of events in the sinφ cosφ variable, where φ is the angle between the π+ π− and the e+ e− decay planes in the kaon centre of mass, is found to exhibit a large CP-violating asymmetry with the value Aφ = (14.2 ± 3.6)%. For the KS → π+ π− e+ e− decay channel, 621 candidates have been identified in the 1999 data sample with an estimated background contribution of 0.7 event. The corresponding branching ratio has been determined to be BR(KS → π+ π− e+ e−) = (4.71 ± 0.32) × 10^−5 . The combined value of this measurement with the published 1998 result is BR(KS → π+ π− e+ e−) = (4.69 ± 0.30) × 10^−5 . No asymmetry is observed in this decay mode. Our results are in good agreement with theoretical predictions based on a phenomenological description of radiative kaon decays. The form factor parameters a1/a2 and gM1 in the KL → π+ π− e+ e− direct emission process as well as the value of the K0 charge radius have been extracted from the data

Production and processing of graphene and related materials

We present an overview of the main techniques for production and processing of graphene and related materials (GRMs), as well as the key characterization procedures. We adopt a 'hands-on' approach, providing practical details and procedures as derived from literature as well as from the authors' experience, in order to enable the reader to reproduce the results. Section I is devoted to 'bottom up' approaches, whereby individual constituents are pieced together into more complex structures. We consider graphene nanoribbons (GNRs) produced either by solution processing or by on-surface synthesis in ultra high vacuum (UHV), as well carbon nanomembranes (CNM). Production of a variety of GNRs with tailored band gaps and edge shapes is now possible. CNMs can be tuned in terms of porosity, crystallinity and electronic behaviour. Section II covers 'top down' techniques. These rely on breaking down of a layered precursor, in the graphene case usually natural crystals like graphite or artificially synthesized materials, such as highly oriented pyrolythic graphite, monolayers or few layers (FL) flakes. The main focus of this section is on various exfoliation techniques in a liquid media, either intercalation or liquid phase exfoliation (LPE). The choice of precursor, exfoliation method, medium as well as the control of parameters such as time or temperature are crucial. A definite choice of parameters and conditions yields a particular material with specific properties that makes it more suitable for a targeted application. We cover protocols for the graphitic precursors to graphene oxide (GO). This is an important material for a range of applications in biomedicine, energy storage, nanocomposites, etc. Hummers' and modified Hummers' methods are used to make GO that subsequently can be reduced to obtain reduced graphene oxide (RGO) with a variety of strategies. GO flakes are also employed to prepare three-dimensional (3d) low density structures, such as sponges, foams, hydro- or aerogels. The assembly of flakes into 3d structures can provide improved mechanical properties. Aerogels with a highly open structure, with interconnected hierarchical pores, can enhance the accessibility to the whole surface area, as relevant for a number of applications, such as energy storage. The main recipes to yield graphite intercalation compounds (GICs) are also discussed. GICs are suitable precursors for covalent functionalization of graphene, but can also be used for the synthesis of uncharged graphene in solution. Degradation of the molecules intercalated in GICs can be triggered by high temperature treatment or microwave irradiation, creating a gas pressure surge in graphite and exfoliation. Electrochemical exfoliation by applying a voltage in an electrolyte to a graphite electrode can be tuned by varying precursors, electrolytes and potential. Graphite electrodes can be either negatively or positively intercalated to obtain GICs that are subsequently exfoliated. We also discuss the materials that can be amenable to exfoliation, by employing a theoretical data-mining approach. The exfoliation of LMs usually results in a heterogeneous dispersion of flakes with different lateral size and thickness. This is a critical bottleneck for applications, and hinders the full exploitation of GRMs produced by solution processing. The establishment of procedures to control the morphological properties of exfoliated GRMs, which also need to be industrially scalable, is one of the key needs. Section III deals with the processing of flakes. (Ultra)centrifugation techniques have thus far been the most investigated to sort GRMs following ultrasonication, shear mixing, ball milling, microfluidization, and wet-jet milling. It allows sorting by size and thickness. Inks formulated from GRM dispersions can be printed using a number of processes, from inkjet to screen printing. Each technique has specific rheological requirements, as well as geometrical constraints. The solvent choice is critical, not only for the GRM stability, but also in terms of optimizing printing on different substrates, such as glass, Si, plastic, paper, etc, all with different surface energies. Chemical modifications of such substrates is also a key step. Sections IV–VII are devoted to the growth of GRMs on various substrates and their processing after growth to place them on the surface of choice for specific applications. The substrate for graphene growth is a key determinant of the nature and quality of the resultant film. The lattice mismatch between graphene and substrate influences the resulting crystallinity. Growth on insulators, such as SiO2, typically results in films with small crystallites, whereas growth on the close-packed surfaces of metals yields highly crystalline films. Section IV outlines the growth of graphene on SiC substrates. This satisfies the requirements for electronic applications, with well-defined graphene-substrate interface, low trapped impurities and no need for transfer. It also allows graphene structures and devices to be measured directly on the growth substrate. The flatness of the substrate results in graphene with minimal strain and ripples on large areas, allowing spectroscopies and surface science to be performed. We also discuss the surface engineering by intercalation of the resulting graphene, its integration with Si-wafers and the production of nanostructures with the desired shape, with no need for patterning. Section V deals with chemical vapour deposition (CVD) onto various transition metals and on insulators. Growth on Ni results in graphitized polycrystalline films. While the thickness of these films can be optimized by controlling the deposition parameters, such as the type of hydrocarbon precursor and temperature, it is difficult to attain single layer graphene (SLG) across large areas, owing to the simultaneous nucleation/growth and solution/precipitation mechanisms. The differing characteristics of polycrystalline Ni films facilitate the growth of graphitic layers at different rates, resulting in regions with differing numbers of graphitic layers. High-quality films can be grown on Cu. Cu is available in a variety of shapes and forms, such as foils, bulks, foams, thin films on other materials and powders, making it attractive for industrial production of large area graphene films. The push to use CVD graphene in applications has also triggered a research line for the direct growth on insulators. The quality of the resulting films is lower than possible to date on metals, but enough, in terms of transmittance and resistivity, for many applications as described in section V. Transfer technologies are the focus of section VI. CVD synthesis of graphene on metals and bottom up molecular approaches require SLG to be transferred to the final target substrates. To have technological impact, the advances in production of high-quality large-area CVD graphene must be commensurate with those on transfer and placement on the final substrates. This is a prerequisite for most applications, such as touch panels, anticorrosion coatings, transparent electrodes and gas sensors etc. New strategies have improved the transferred graphene quality, making CVD graphene a feasible option for CMOS foundries. Methods based on complete etching of the metal substrate in suitable etchants, typically iron chloride, ammonium persulfate, or hydrogen chloride although reliable, are time- and resource-consuming, with damage to graphene and production of metal and etchant residues. Electrochemical delamination in a low-concentration aqueous solution is an alternative. In this case metallic substrates can be reused. Dry transfer is less detrimental for the SLG quality, enabling a deterministic transfer. There is a large range of layered materials (LMs) beyond graphite. Only few of them have been already exfoliated and fully characterized. Section VII deals with the growth of some of these materials. Amongst them, h-BN, transition metal tri- and di-chalcogenides are of paramount importance. The growth of h-BN is at present considered essential for the development of graphene in (opto) electronic applications, as h-BN is ideal as capping layer or substrate. The interesting optical and electronic properties of TMDs also require the development of scalable methods for their production. Large scale growth using chemical/physical vapour deposition or thermal assisted conversion has been thus far limited to a small set, such as h-BN or some TMDs. Heterostructures could also be directly grown. Section VIII discusses advances in GRM functionalization. A broad range of organic molecules can be anchored to the sp2 basal plane by reductive functionalization. Negatively charged graphene can be prepared in liquid phase (e.g. via intercalation chemistry or electrochemically) and can react with electrophiles. This can be achieved both in dispersion or on substrate. The functional groups of GO can be further derivatized. Graphene can also be noncovalently functionalized, in particular with polycyclic aromatic hydrocarbons that assemble on the sp2 carbon network by π–π stacking. In the liquid phase, this can enhance the colloidal stability of SLG/FLG. Approaches to achieve noncovalent on-substrate functionalization are also discussed, which can chemically dope graphene. Research efforts to derivatize CNMs are also summarized, as well as novel routes to selectively address defect sites. In dispersion, edges are the most dominant defects and can be covalently modified. This enhances colloidal stability without modifying the graphene basal plane. Basal plane point defects can also be modified, passivated and healed in ultra-high vacuum. The decoration of graphene with metal nanoparticles (NPs) has also received considerable attention, as it allows to exploit synergistic effects between NPs and graphene. Decoration can be either achieved chemically or in the gas phase. All LMs, can be functionalized and we summarize emerging approaches to covalently and noncovalently functionalize MoS2 both in the liquid and on substrate. Section IX describes some of the most popular characterization techniques, ranging from optical detection to the measurement of the electronic structure. Microscopies play an important role, although macroscopic techniques are also used for the measurement of the properties of these materials and their devices. Raman spectroscopy is paramount for GRMs, while PL is more adequate for non-graphene LMs (see section IX.2). Liquid based methods result in flakes with different thicknesses and dimensions. The qualification of size and thickness can be achieved using imaging techniques, like scanning probe microscopy (SPM) or transmission electron microscopy (TEM) or spectroscopic techniques. Optical microscopy enables the detection of flakes on suitable surfaces as well as the measurement of optical properties. Characterization of exfoliated materials is essential to improve the GRM metrology for applications and quality control. For grown GRMs, SPM can be used to probe morphological properties, as well as to study growth mechanisms and quality of transfer. More generally, SPM combined with smart measurement protocols in various modes allows one to get obtain information on mechanical properties, surface potential, work functions, electrical properties, or effectiveness of functionalization. Some of the techniques described are suitable for 'in situ' characterization, and can be hosted within the growth chambers. If the diagnosis is made 'ex situ', consideration should be given to the preparation of the samples to avoid contamination. Occasionally cleaning methods have to be used prior to measurement