Fiber Strong Shape Theory for Topological Spaces

In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space \Bo. Our approach is based on the method of Marde\v{s}i\'{c}-Lisica and instead of resolutions, introduced by Marde\v{s}i\'{c}, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over \Bo which is coarser than the classification of spaces over \Bo induced by fiber homotopy theory, but is finer than the classification of spaces over \Bo given by usual fiber shape theory

Theory of phonon-assisted "forbidden" optical transitions in spin-gapped systems

We consider the absorption of light with emission of one S(tot)=1 magnetic excitation in systems with a spin gap induced by quantum fluctuations. We argue that an electric dipole transition is allowed on the condition that a virtual phonon instantaneously breaks the inversion symmetry. We derive an effective operator for the transition and argue that the proposed theory explains the polarized experiments in CuGeO(3) and SrCu(2)[BO(3)](2).Comment: 9 pages, 4 figure

Emergence of One-Dimensional Physics from the Distorted Shastry-Sutherland Lattice

Motivated by the on-going investigation of SrCu$_2$(BO$_3$)$_2$ under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/2 model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective S=1 Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.Comment: 4 pages, 5 figure

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Chemical compositions of six metal-poor stars in the ultra-faint dwarf spheroidal galaxy Bo\"otes I

Ultra-faint dwarf galaxies recently discovered around the Milky Way (MW) contain extremely metal-poor stars, and might represent the building blocks of low-metallicity components of the MW. Among them, the Bo\"otes I dwarf spheroidal galaxy is of particular interest because of its exclusively old stellar population. We determine chemical compositions of six red giant stars in Bo\"otes I, based on the high-resolution spectra obtained with the High Dispersion Spectrograph mounted on the Subaru Telescope. Abundances of 12 elements, including C, Na, alpha, Fe-peak, and neutron capture elements, were determined for the sample stars. The abundance results were compared to those in field MW halo stars previously obtained using an abundance analysis technique similar to the present study. We confirm the low metallicity of Boo-094 ([Fe/H]=-3.4). Except for this star, the abundance ratios ([X/Fe]) of elements lighter than zinc are generally homogeneous with small scatter around the mean values in the metallicities spanned by the other five stars (-2.7-2.7 show no significant enhancement of carbon. The [Mg/Fe] and [Ca/Fe] ratios are almost constant with a modest decreasing trend with increasing [Fe/H] and are slightly lower than the field halo stars. The [Sr/Fe] and [Sr/Ba] ratios also tend to be lower in the Bo\"otes I stars than in the halo stars. Our results of small scatter in the [X/Fe] ratios for elements lighter than zinc suggest that these abundances were homogeneous among the ejecta of prior generation(s) of stars in this galaxy.Comment: 16 pages, 12 figures. Accepted to A&A, language correcte