On Semimonotone Matrices, $$R_0$$ -Matrices and Q-Matrices

Journal of Optimization Theory and Applications - In 1979, Pang proved that within the class of semimonotone matrices, $$R_0$$ -matrices are Q-matrices and conjectured that the converse is also...     

Improper hydrogen bonding and motional narrowing in binary mixtures of 2‐ and 3‐bromopyridine in methanol probed by polarized Raman study and DFT calculations

A concentration‐dependent Raman study of the ν(C Br) stretching and trigonal bending modes of 2‐ and 3‐Br‐pyridine (2Br‐p and 3Br‐p) in CH₃OH was performed at different mole fractions of the reference molecule, 2Br‐p/3Br‐p, from 0.1 to 0.9 in order to understand the origin of blue/red wavenumber shifts of the vibrational modes due to hydrogen‐bond formation. The appearance of additional Raman bands in these binary systems at ∼617 cm⁻¹in the case of 2Br‐p and at ∼618 cm⁻¹ in the case of 3Br‐p compared to neat bromopyridine derivatives were attributed to specific hydrogen‐bonded complexes formed in the mixtures. The interpretation of experimental results is supported by density functional calculations on optimized geometries and vibrational wavenumbers of 2Br‐p and 3Br‐p and a series of hydrogen‐bonded complexes with methanol. The parameters obtained from these calculations were used for a qualitative explanation of the blue/red shifts. The wavenumber shifts and linewidth changes for the ν(C Br) stretching and trigonal bending modes as a function of concentration reveal that the caging effects leading to motional narrowing and diffusion‐causing line broadening are simultaneously operative, in addition to the blue shift caused due to hydrogen bonding. Copyright © 2007 John Wiley & Sons, Ltd.     

The Boulware–Deser class of spacetimes radiates

We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Optical diffraction in twisted liquid-crystalline media-phase grating mode

We have calculated the diffraction of light perpendicular to the twist axis in a chiral smectic C liquid crystal. In contrast to a cholesteric liquid crystal, in a chiral smectic C liquid crystal we find extra orders which form the odd orders in the diffraction pattern. For an incident linearly polarized light, at a general azimuth, these odd orders are linearly polarized and the even orders are elliptically polarized. The intensities of the odd orders are always independent of the azimuth of the incident light, while this is possible for even orders only at a particular tilt angle of the chiral smectic C liquid crystal. Also, for the incident vibration parallel or perpendicular to the twist axis the odd orders are polarized in the orthogonal linear state with respect to incident vibration, while the even orders are in the same linear state.     

Wild African elephants (Loxodonta africana) discriminate between familiar and unfamiliar conspecific seismic alarm calls

The ability to discriminate between call types and callers as well as more subtle information about the importance of a call has been documented in a range of species. This type of discrimination is also important in the vibrotactile environment for species that communicate via vibrations. It has recently been shown that African elephants (Loxodonta africana) can detect seismic cues, but it is not known whether they discriminate seismic information from noise. In a series of experiments, familiar and unfamiliar alarm calls were transmitted seismically to wild African elephant family groups. Elephants respond significantly to the alarm calls of familiar herds (p=0.004) but not to the unfamiliar calls and two different controls, thus demonstrating the ability of elephants to discriminate subtle differences between seismic calls given in the same context. If elephants use the seismic environment to detect and discriminate between conspecific calls, based on the familiarity of the caller or some other physical property, they may be using the ground as a very sophisticated sounding board.