Additive results for the group inverse in an algebra with applications to block operators

We derive a very short expression for the group inverse of a(1) + ... + a(n) when a(1), ... , a(n) are elements in an algebra having group inverse and satisfying a(i)a(j) = 0 for i C∗-algebras. Journal of Mathematical Analysis and Applications, 345(2), 766-770. doi:10.1016/j.jmaa.2008.04.062Benítez, J, Liu, X and Zhu, T.Nonsingularity and group invertibility of linear combinations of two k-potent matrices, Linear Multilinear Algebra (accepted)Castro-González, N., Dopazo, E., & Martínez-Serrano, M. F. (2009). On the Drazin inverse of the sum of two operators and its application to operator matrices. Journal of Mathematical Analysis and Applications, 350(1), 207-215. doi:10.1016/j.jmaa.2008.09.035González, N. C., & Koliha, J. J. (2004). New additive results for the g-Drazin inverse. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 134(6), 1085-1097. doi:10.1017/s0308210500003632Cvetković-Ilić, D. S., Djordjević, D. S., & Wei, Y. (2006). Additive results for the generalized Drazin inverse in a Banach algebra. Linear Algebra and its Applications, 418(1), 53-61. doi:10.1016/j.laa.2006.01.015Deng, C. Y. (2009). The Drazin inverses of sum and difference of idempotents. Linear Algebra and its Applications, 430(4), 1282-1291. doi:10.1016/j.laa.2008.10.017Deng, C, Cvetković-Ilić, DS and Wei, Y.Some results on the generalized Drazin inverse of operator matrices, Linear Multilinear Algebra (2009). DOI: 10.1080/03081080902722642Djordjević, D. S., & Wei, Y. (2002). Additive results for the generalized Drazin inverse. Journal of the Australian Mathematical Society, 73(1), 115-126. doi:10.1017/s1446788700008508Hartwig, R. E., Wang, G., & Wei, Y. (2001). Some additive results on Drazin inverse. Linear Algebra and its Applications, 322(1-3), 207-217. doi:10.1016/s0024-3795(00)00257-3Koliha, J. J. (2000). Elements of C*-algebras commuting with their Moore-Penrose inverse. Studia Mathematica, 139(1), 81-90. doi:10.4064/sm-139-1-81-9

Fluctuations in granular gases

A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we present numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure

Invasive nasal histiocytic sarcoma as a cause of temporal lobe epilepsy in a cat

Case summary A 10-year-old neutered female domestic shorthair cat was presented with an acute onset of neurological signs suggestive of a right-sided forebrain lesion, temporal lobe epilepsy and generalised seizure activity. MRI of the head revealed an expansile soft tissue mass in the caudal nasal passages (both sides but predominantly right-sided) involving the ethmoid bone and extending through the cribriform plate into the cranial vault affecting predominantly the right frontal lobe and temporal lobe. Histopathological examination of the tumour revealed a histiocytic sarcoma. Relevance and novel information This is the first report of a cat with clinical signs of temporal lobe epilepsy due to an invasive, histiocytic sarcoma. Histiocytic sarcoma, although rare, should be included in the list of differential diagnoses for soft tissue masses extending through the cribriform plate. Other differential diagnoses are primary nasal neoplasia (eg, adenocarcinoma, squamous cell carcinoma, chondrosarcoma and other types of sarcomas), lymphoma and olfactory neuroblastoma. Temporal lobe epilepsy in cats can be the consequence of primary pathology of temporal lobe structures, or it can be a consequence of pathology with an effect on these structures (eg, mass effect or disruption of interconnecting neuronal pathways)

Forecasting Tunisian type 2 diabetes prevalence to 2027: validation of a simple model.

BACKGROUND: Most projections of type 2 diabetes (T2D) prevalence are simply based on demographic change (i.e. ageing). We developed a model to predict future trends in T2D prevalence in Tunisia, explicitly taking into account trends in major risk factors (obesity and smoking). This could improve assessment of policy options for prevention and health service planning. METHODS: The IMPACT T2D model uses a Markov approach to integrate population, obesity and smoking trends to estimate future T2D prevalence. We developed a model for the Tunisian population from 1997 to 2027, and validated the model outputs by comparing with a subsequent T2D prevalence survey conducted in 2005. RESULTS: The model estimated that the prevalence of T2D among Tunisians aged over 25 years was 12.0% in 1997 (95% confidence intervals 9.6%-14.4%), increasing to 15.1% (12.5%-17.4%) in 2005. Between 1997 and 2005, observed prevalence in men increased from 13.5% to 16.1% and in women from 12.9% to 14.1%. The model forecast for a dramatic rise in prevalence by 2027 (26.6% overall, 28.6% in men and 24.7% in women). However, if obesity prevalence declined by 20% in the 10 years from 2013, and if smoking decreased by 20% over 10 years from 2009, a 3.3% reduction in T2D prevalence could be achieved in 2027 (2.5% in men and 4.1% in women). CONCLUSIONS: This innovative model provides a reasonably close estimate of T2D prevalence for Tunisia over the 1997-2027 period. Diabetes burden is now a significant public health challenge. Our model predicts that this burden will increase significantly in the next two decades. Tackling obesity, smoking and other T2D risk factors thus needs urgent action. Tunisian decision makers have therefore defined two strategies: obesity reduction and tobacco control. Responses will be evaluated in future population surveys

Intrinsic strong light-matter coupling with self-hybridized bound states in the continuum in van der Waals metasurfaces.

Photonic bound states in the continuum (BICs) provide a standout platform for strong light-matter coupling with transition metal dichalcogenides (TMDCs) but have so far mostly been implemented as traditional all-dielectric metasurfaces with adjacent TMDC layers, incurring limitations related to strain, mode overlap and material integration. Here, we demonstrate intrinsic strong coupling in BIC-driven metasurfaces composed of nanostructured bulk tungsten disulfide (WS2) and exhibiting resonances with sharp, tailored linewidths and selective enhancement of light-matter interactions. Tuning of the BIC resonances across the exciton resonance in bulk WS2 is achieved by varying the metasurface unit cells, enabling strong coupling with an anticrossing pattern and a Rabi splitting of 116 meV. Crucially, the coupling strength itself can be controlled and is shown to be independent of material-intrinsic losses. Our self-hybridized metasurface platform can readily incorporate other TMDCs or excitonic materials to deliver fundamental insights and practical device concepts for polaritonic applications

Transport coefficients for inelastic Maxwell mixtures

The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are {\em exactly} obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux.Comment: 9 figures, to be published in J. Stat. Phy

Resolving debris discs in the far-infrared: early highlights from the DEBRIS survey

We present results from the earliest observations of DEBRIS, a Herschel Key Programme to conduct a volume- and flux-limited survey for debris discs in A-type through M-type stars. PACS images (from chop/nod or scan-mode observations) at 100 and 160 micron are presented toward two A-type stars and one F-type star: beta Leo, beta UMa and eta Corvi. All three stars are known disc hosts. Herschel spatially resolves the dust emission around all three stars (marginally, in the case of beta UMa), providing new information about discs as close as 11 pc with sizes comparable to that of the Solar System. We have combined these data with existing flux density measurements of the discs to refine the SEDs and derive estimates of the fractional luminosities, temperatures and radii of the discs.Comment: to be published in A&A, 5 pages, 2 color figure