On ``Time-Periodic' Black-Hole Solutions to Certain Spherically Symmetric Einstein-Matter Systems

This paper explores black hole solutions of various Einstein-wave matter systems admitting a time-orientation preserving isometry of their domain of outer communications taking some point to its future. In the first two parts, it is shown that such solutions, assuming in addition that they are spherically symmetric and the matter has a certain structure, must be Schwarzschild or Reissner-Nordström. Non-trivial examples of matter for which the result applies are a wave map and a massive charged scalar field interacting with an electromagnetic field. The results thus generalize work of Bekenstein [1] and Heusler [13] from the static to the periodic case. In the third part, which is independent of the first two, it is shown that Dirac fields preserved by an isometry of a spherically symmetric domain of outer communications of the type described above must vanish. It can be applied in particular to the Einstein-Dirac-Maxwell equations or the Einstein-Dirac-Yang/Mills equations, generalizing work of Finster, Smoller and Yau [10, 8, 9 and also 7].     

Thermal desorption/gas chromatography/mass spectrometry approach for characterization of the volatile fraction from amber specimens: A possibility of tracking geological origins

Research on the chemical composition of fossil resins has evolved during the last decades as a multidisciplinary field and is strongly oriented toward the correlation with their geological and botanical origin. Various extraction procedures and chromatographic techniques have been used together for identifying the volatile compounds contained in the fossil resin matrix. Hyphenation between thermal desorption (TD), gas chromatography (GC) and mass spectrometry detection (MS) has been chosen to investigate the volatile compounds fraction from ambers with a focus on Romanite (Romanian amber) and Baltic amber species. A data analysis procedure was developed for the main purpose of fingerprinting ambers based on the MS identity of the peaks generated by the volatile fraction, together with their relative percentual area within the chromatogram. Chromatographic data analysis was based entirely on Automated Mass Spectral Deconvolution & Identification System (AMDIS) software to produce deconvoluted mass spectra which were used to build-up a mixed mass spectra and relative retention scale library. Multivariate data analysis was further applied on AMDIS results with successful discrimination between Romanite and Baltic ambers. A special trial was conducted to generate pyrolysis “like” macromolecular structure breakdown to volatile compounds by gamma irradiation with a high absorbed dose of 500 kGy. Contrary to our expectations the volatile fraction fingerprints were not modified after irradiation experiments. A complementary non-destructive new approach by ESR spectroscopy was also proposed for discriminating between Romanite and Baltic ambers.     

On induced modules and tableaux for the special orthogonal groups

In a recent article, King and Welsh prove a standard basis theorem for the orthogonal groups over a field of characteristic zero utilizing certain tableaux of Proctor that are related to Gelfand patterns. The purpose of the present paper is to extend the previous result to the case of any characteristic other than 2 by working within the context of induced modules for the special orthogonal groups.     

Influence of aggregates and solvent aromaticity on the emission of conjugated polymers

The influence of aggregates and solvent aromaticity on the photophysics and fluorescence dynamics of two conjugated polymers is studied. The two polymers are derivatives of poly(p-phenylene vinylene) (PPV) containing different kinked moieties along the main chain. The polymers contain 2,6-diphenylpyridine and m-terphenyl kinked moieties and they are abbreviated as PN and PC, respectively. The insertion of kinked segments along the main chain shifts the emission spectrum from the yellow-orange spectral region, common to PPV derivatives, to the blue-green spectral region. The results show that in dilute solutions the polymers decay monoexponentially, while in concentrated ones the fluorescence decays biexponentially, indicating fluorescence quenching. This is attributed to an energy transfer process from polymer chains to aggregates that occurs within a few tens of picoseconds. By comparing the photophysics and fluorescence dynamics of polymer PN in a nonaromatic and an aromatic solvent, we conclude that the polymer conformation adopted in the aromatic solvent leads to a higher fluorescence quantum yield and a longer fluorescence lifetime. Furthermore, the fluorescence quenching of PN because of aggregates is faster and more efficient in the aromatic than in the nonaromatic solvent. These results can be explained through a more extended chain conformation of PN in the aromatic solvent.     

Femtosecond time resolved fluorescence dynamics of a cationic water-soluble poly(fluorenevinylene-co-phenylenevinylene)

A recently synthesized cationic water-soluble poly(fluorenevinylene-co-phenylenevinylene) was studied by means of steady state and femtosecond time resolved upconversion spectroscopy in aqueous and EtOH solutions. Steady state spectroscopic measurements showed that the polymer emits at the blue-green spectral region and that aggregates are formed in concentrated polymer solutions. The fluorescence dynamics of the polymer in concentrated solutions, studied at a range of emission wavelengths, exhibited a wavelength dependent and multiexponential decay, indicating the existence of various decay mechanisms. Specifically, a rapid decay at short emission wavelengths and a slow rise at long wavelengths were observed. Both features reveal an energy transfer process from isolated to aggregated chains. The contribution of the energy transfer process as well as of the isolated chains and the aggregates on the overall fluorescence decay of the polymer was determined. The dependence of the energy transfer rate and efficiency on polymer concentration was also examined.     

Photophysics of 9,9-Dimethylacridan-Substituted Phenylstyrylpyrimidines Exhibiting Long-Lived Intramolecular Charge-Transfer Fluorescence and Aggregation-Induced Emission Characteristics

Six pyrimidine-based push–pull systems substituted at positions C2 and C4/6 with phenylacridan and styryl moieties, employing methoxy or N,N-diphenylamino donors, have been designed and synthesized through cross-coupling and Knoevenagel reactions. X-ray analysis confirmed that the molecular structure featured the acridan moiety arranged perpendicularly to the residual π system. Photophysical studies revealed significant differences between the methoxy and N,N-diphenylamino chromophores. Solvatochromic studies revealed that the methoxy derivatives showed dual emission in polar solvents. Time-resolved spectroscopy revealed that the higher energy band involved very fast (<80 ps) fluorescence, whereas the lower energy one included long components (≈30 ns) due to long-lived intramolecular charge-transfer fluorescence. In contrast to N,N-diphenylamino chromophores, the methoxy derivatives also showed aggregation-induced emission in mixtures of THF/water, as well as dual emission in thin films, covering almost the whole visible spectrum with corresponding chromaticity coordinates not far from that of pure white light. These properties render the methoxy derivatives as very promising organic materials for white organic light-emitting diodes.     

On the Residual Finiteness of Outer Automorphisms of Hyperbolic Groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite.     

Social media and sensemaking patterns in new product development: demystifying the customer sentiment

Artificial intelligence by principle is developed to assist but also support decision making processes. In our study, we explore how information retrieved from social media can assist decision-making processes for new product development (NPD). We focus on consumers’ emotions that are expressed through social media and analyse the variations of their sentiments in all the stages of NPD. We collect data from Twitter that reveal consumers’ appreciation of aspects of the design of a newly launched model of an innovative automotive company. We adopt the sensemaking approach coupled with the use of fuzzy logic for text mining. This combinatory methodological approach enables us to retrieve consensus from the data and to explore the variations of sentiments of the customers about the product and define the polarity of these emotions for each of the NPD stages. The analysis identifies sensemaking patterns in Twitter data and explains the NPD process and the associated steps where the social interactions from customers can have an iterative role. We conclude the paper by outlining an agenda for future research in the NPD process and the role of the customer opinion through sensemaking mechanisms.

     

The red‐shift effect and radiation decay on black hole spacetimes

We consider solutions to the linear wave equation □_g? = 0 on a (maximally extended) Schwarzschild spacetime with parameter M > 0, evolving from sufficiently regular initial data prescribed on a complete Cauchy surface Σ, where the data are assumed only to decay suitably at spatial infinity. (In particular, the support of ? may contain the bifurcate event horizon.) It is shown that the energy flux F(??) of the solution (as measured by a strictly timelike T? that asymptotically matches the static Killing field) through arbitrary achronal subsets ?? of the black hole exterior region satisfies the bound F(??) ≤ C E(v + u), where v and u denote the infimum of the Eddington‐Finkelstein advanced and retarded time of ??, v₊ denotes max{1, v}, and u₊ denotes max{1, u}, where C is a constant depending only on the parameter M, and E depends on a suitable norm of the solution on the hypersurface t ? u + v = 1. (The bound applies in particular to subsets ?? of the event horizon or null infinity.) It is also shown that ? satisfies the pointwise decay estimate |?| ≤ C Ev in the entire exterior region, and the estimates |r?| ≤ C_R?E(1 + |u|)^?1/2 and |r^1/2?| ≤ C_R?Eu in the region {r ≥ R?} ∩ J⁺(Σ) for any R? > 2M. The estimates near the event horizon exploit an integral energy identity normalized to local observers. This estimate can be thought to quantify the celebrated red‐shift effect. The results in particular give an independent proof of the classical result |?| ≥ C E of Kay and Wald without recourse to the discrete isometries of spacetime. © 2009 Wiley Periodicals, Inc.