Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.     

Nonlinear shear‐free radiative collapse

We study realistic models of relativistic radiating stars undergoing gravitational collapse which have vanishing Weyl tensor components. Previous investigations are generalized by retaining the inherent nonlinearity at the boundary. We transform the boundary condition to an Abel equation of the first kind. A variety of nonlinear solutions is generated all of which can be written explicitly. Several classes of infinite solutions exist. Copyright © 2007 John Wiley & Sons, Ltd.     

The Plateau-Douglas problem for nonorientable minimal surfaces

In this paper, the solution of the Plateau-Douglas problem is presented for nonorientable minimal surfaces of higher genus in Riemannian manifolds.     

Electron transfer contributions to the quenching of aromatic ketone phosphorescence by electron—poor olefins

The rate constant k_ir for quenching diaryl ketone triplet states by electron poor olefins in CCl₄ at room temperature decreases with decreasing reduction potential of the olefin. Unlike in previous cases, our data here fit the Weller equation, which predicts that en k_ir ≈ 1/RT.     

Identification and synthesis of novel biomaterials based on spider structural silk fibers

The diversity in function and mechanical behavior of spider silks, and the ability to produce these silks recombinantly, have tremendous potential in creating a new class of biomimetic materials. Here we investigate the structural and mechanical properties of pyriform silks from the golden orb-weaver, Nephila clavipes. Nanoscale indentation measurements using atomic force microscopy on natural pyriform silk suggests that this biomaterial has high toughness that may be suitable for dissipating high amounts of mechanical energy. We also observed the occurrence of highly organized nanocrystals within the pyriform silk fibers that may contribute to the remarkable energy dissipation capability of these silks. It has been demonstrated that poly-(Gly–Ala) and poly-Ala stretches within the internal block repeat modules of dragline silk fibroins form nanocrystals, and these nanocrystalline structures may be responsible for the high extensibility of the dragline silks. In contrast, amino acid sequence analysis shows that PySp2 does not contain the same motifs. In the absence of poly-(Gly–Ala) and poly-Ala repeats, we hypothesized that PySp2 contains new protein motifs sufficient to polymerize into functional structures. To investigate the functional contributions of these novel motifs during pyriform fiber formation, we expressed different recombinant PySp2 fibroins with various segments spanning its block repeat units. We demonstrate that PySp2 recombinant proteins with the Pro-rich sub-block domain (PXP motifs, where X= sub-set of the amino acids A, L, or R) and/or the Ser + Gln + Ala-rich sub-block domain (QQSSVAQS motifs) are sufficient for artificial fiber formation. Moreover, we show that recombinant PySp2 proteins that contain a single block repeat unit can self-assemble into foam-like nanostructures. Collectively, our findings support the use of PySp2 recombinant proteins for a wide range of biomimetic materials with morphologies ranging from fibers to porous structures.     

Radical Protection by Differently Composed Creams in the UV/VIS and IR Spectral Ranges

Modern sunscreens are well suited to provide sufficient protection in the UV range because the filter substances absorb or scatter UV radiation. Although up to 50% of radicals are formed in the visible and infrared spectral range during solar radiation protection strategies are not provided in this range. Previous investigations of commercially available products have shown that in addition to physical filters, antioxidants (AO) are necessary to provide protective effects in the infrared range by neutralizing already formed radicals. In this study, the efficacy of filter substances and AO to reduce radical formation in both spectral ranges was investigated after UV/VIS or IR irradiation. Optical properties and radical protection were determined for the investigated creams. It was found that organic UV filters lower radical formation in the UV/VIS range to 35% compared to untreated skin, independent of the presence of AO. Further reduction to 14% was reached by addition of 2% physical filters, whereas physical filters alone were ineffective in the UV/VIS range due to the low concentration. In contrast, this filter type reduced radical formation in the IR range significantly to 65%; similar effects were aroused after application of AO. Sunscreens which contain organic UV filters, physical filters and AO ensure protection in the complete solar spectrum.     

Wavelet‐based self‐organizing maps for classifying multivariate time series

Following a nonparametric approach, we suggest a time‐series clustering method. Our clustering approach combines the benefits connected to the interpretative power of the nonparametric representation of the time series, and the clustering and vector quantization informational gain produced by the adopted unsupervised neural networks technique, enhanced with the self‐organizing maps ordering and topological preservation abilities. The proposed clustering method takes into account a composite wavelet‐based information of the multivariate time series by adding to the information connected to the wavelet variance, namely the influence of variability of individual univariate components of the multivariate time series across scales, the information associated to wavelet correlation, represented by the interaction between pairs of univariate components of the multivariate time series at each scale, and then suitably tuning the combination of these pieces of information. In order to assess the effectiveness of the proposed clustering approach, a simulation study and an empirical application are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

Unsteady thermal boundary-layer on an infinite yawed wedge whose temperature gradient is prescribed

In this paper, the temperature distribution at the surface of an infinite yawed wedge, when temperature of the main-stream is constant, is studied under two cases; one when temperature gradient of the wall is steady and the velocity of the main-stream is unsteady, and the other when temperature gradient of the wall is unsteady and the velocity of the main-stream is steady. It is found that the heat transfer depends on the wedge angle, the angle parameter and the yaw of the wedge. The behaviour with these parameters are studied and are illustrated graphically.     

Bivariate hypergeometric D-modules

We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank.