On Fujita invariants of subvarieties of a uniruled variety

We show that if $X$ is a smooth uniruled projective variety and $L$ a big and semiample $\mathbb{Q}$-divisor on $X$, then there exists a proper closed subset $W\subset X$ such that every subvariety $Y$ satisfying $a(Y,L)> a(X,L)$ is contained in $W$.Comment: 6 pages. Comments are welcome; v2: 7 pages, proof rewritte

Hierarchical video summarisation in reference frame subspace

In this paper, a hierarchical video structure summarization approach using Laplacian Eigenmap is proposed, where a small set of reference frames is selected from the video sequence to form a reference subspace to measure the dissimilarity between two arbitrary frames. In the proposed summarization scheme, the shot-level key frames are first detected from the continuity of inter-frame dissimilarity, and the sub-shot level and scene level representative frames are then summarized by using k-mean clustering. The experiment is carried on both test videos and movies, and the results show that in comparison with a similar approach using latent semantic analysis, the proposed approach using Laplacian Eigenmap can achieve a better recall rate in keyframe detection, and gives an efficient hierarchical summarization at sub shot, shot and scene levels subsequently

On the masses of black-holes in radio-loud quasars

The central black-hole masses of a sample of radio-loud quasars are estimated by using the data of $H_{\beta}$ line-width and the optical continuum luminosity. The vast majority of the quasars in this sample have black-hole masses larger than $10^{8} M_{\odot}$, while a few quasars may contain relatively smaller black-holes. We found a significant anti-correlation between the radio-loudness and the central black-hole mass. It might imply that the jet formation is governed by the black-hole mass.Comment: 5 pages, two figures are added, accepted by MNRAS Letter

Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

In a previous note [Ru] the susceptibility function was analyzed for some examples of maps of the interval. The purpose of the present note is to give a concise treatment of the general unimodal Markovian case (assuming $f$ real analytic). We hope that it will similarly be possible to analyze maps satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru], application of a theorem of Whitney [Wh] should prove differentiability of the map $f\mapsto\rho_f$ restricted to a suitable set.Comment: 8 page

Classification for the universal scaling of N\'eel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets

Inspired by the recently theoretical development relevant to the experimental data of TlCuCl$_3$, particularly those associated with the universal scaling between the N\'eel temperature $T_N$ and the staggered magnetization density $M_s$, we carry a detailed investigation of 3-dimensional (3D) dimerized quantum antiferromagnets using the first principles quantum Monte Carlo calculations. The motivation behind our study is to better understand the microscopic effects on these scaling relations of $T_N$ and $M_s$, hence to shed some light on some of the observed inconsistency between the theoretical and the experimental results. Remarkably, for the considered 3D dimerized models, we find that the established universal scaling relations can indeed be categorized by the amount of stronger antiferromagnetic couplings connected to a lattice site. Convincing numerical evidence is provided to support this conjecture. The relevance of the outcomes presented here to the experiments of TlCuCl$_3$ is briefly discussed as well.Comment: 9 pages, 27 figure

Study on the thermal stability of Polystyryl surfactants and its modified clay nanocomposites

Five oligomeric styrene surfactants, N,N,N-trimethylpolystyrylammonium, N,N-dimethyl-N-benzylpolystyrylammonium, N,N-dimethyl-N-hexadecylpolystyrylammonium, 1,2-dimethyl-3-polystyrylimidazolium, and triphenylpolystyrylphosphonium chlorides were synthesized and used to prepare organically modified clays. Both styrene and methyl methacrylate nanocomposites were prepared by melt blending and the type of nanocomposite was evaluated by X-ray diffraction and transmission electron microscopy. The thermal stability of the organically modified clays and the nanocomposites were studied by thermogravimetric analysis; these systems do give clays which have good thermal stability and may be useful for melt blending with polymers that must be processed at higher temperatures