An equitriangular integral transform and its applications

Equitriangular integral transform for solving boundary value problems in viscous flow and heat transfe

Hypervelocity binary stars: smoking gun of massive binary black holes

The hypervelocity stars recently found in the Galactic halo are expelled from the Galactic center through interactions between binary stars and the central massive black hole or between single stars and a hypothetical massive binary black hole. In this paper, we demonstrate that binary stars can be ejected out of the Galactic center with velocities up to 10^3 km/s, while preserving their integrity, through interactions with a massive binary black hole. Binary stars are unlikely to attain such high velocities via scattering by a single massive black hole or through any other mechanisms. Based on the above theoretical prediction, we propose a search for binary systems among the hypervelocity stars. Discovery of hypervelocity binary stars, even one, is a definitive evidence of the existence of a massive binary black hole in the Galactic center.Comment: 5 pages, 3 figures, shortened version, ApJL in pres

The Low-level Spectrum of the W3W_3 String

We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.Comment: 31 pages, Plain Tex, CTP TAMU-70/92, Goteborg ITP 92-43, Imperial/TP/91-92/22, KCL-TH-92-

Duration distributions for different softness groups of gamma-ray bursts

Gamma-ray bursts (GRBs) are divided into two classes according to their durations. We investigate if the softness of bursts plays a role in the conventional classification of the objects. We employ the BATSE (Burst and Transient Source Experiment) catalog and analyze the duration distributions of different groups of GRBs associated with distinct softness. Our analysis reveals that the conventional classification of GRBs with the duration of bursts is influenced by the softness of the objects. There exits a bimodality in the duration distribution of GRBs for each group of bursts and the time position of the dip in the bimodality histogram shifts with the softness parameter. Our findings suggest that the conventional classification scheme should be modified by separating the two well-known populations in different softness groups, which would be more reasonable than doing so with a single sample. According to the relation between the dip position and the softness parameter, we get an empirical function that can roughly set apart the short-hard and long-soft bursts: $SP = (0.100 \pm 0.028) T_{90}^{-(0.85 \pm 0.18)}$, where $SP$ is the softness parameter adopted in this paper.Comment: 20 pages, 10 figure

Enthalpies of formation of lanthanide oxyapatite phases

A family of lanthanide silicates adopts an oxyapatite-like structure with structural formula Ln9.33∎0.67(SiO4)6O2 (Ln 4 La, Sm, Nd, Gd, ∎ = vacancy). The enthalpies of solution, DHS, for these materials and their corresponding binary oxides were determined by high-temperature oxide melt solution calorimetry using molten 2PbO·B2O3 at 1078 K. These data were used to complete thermodynamic cycles to calculate enthalpies of formation from the oxides, ΔHs f-oxides (kJ/mol): La9.33∎0.67(SiO4)6O2 = −776.3 ± 17.9, Nd9.33∎0.67(SiO4)6O2 = −760.4 ± 31.9, Sm9.33∎0.67(SiO4)6O2 = −590.3 ± 18.6, and Gd9.33∎0.67(SiO4)6O2 = −446.9 ± 21.9. Reference data were used to calculate the standard enthalpies of formation from the elements, ΔH0 f (kJ/mol): La9.33∎0.67(SiO4)6O2 = −14611.0 ± 19.4, Nd9.33∎0.67(SiO4)6O2 = −14661.5 ± 32.2, Sm9.33∎0.67(SiO4)6O2 = −14561.7 ± 20.8, and Gd9.33∎0.67(SiO4)6O2 = −14402.7 ± 28.2. The formation enthalpies become more endothermic as the ionic radius of the lanthanide ion decreases

Continuum Electromechanical Modeling of Protein-Membrane Interaction

A continuum electromechanical model is proposed to describe the membrane curvature induced by electrostatic interactions in a solvated protein-membrane system. The model couples the macroscopic strain energy of membrane and the electrostatic solvation energy of the system, and equilibrium membrane deformation is obtained by minimizing the electro-elastic energy functional with respect to the dielectric interface. The model is illustrated with the systems with increasing geometry complexity and captures the sensitivity of membrane curvature to the permanent and mobile charge distributions.Comment: 5 pages, 12 figure

Toward a unified theory of sparse dimensionality reduction in Euclidean space

Let $\Phi\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column. For a subset $T$ of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $$\mathop{\mathbb{E}}_\Phi \sup_{x\in T} \left|\|\Phi x\|_2^2 - 1 \right| < \varepsilon ,$$ i.e. so that $\Phi$ preserves the norm of every $x\in T$ simultaneously and multiplicatively up to $1+\varepsilon$. We introduce a new complexity parameter, which depends on the geometry of $T$, and show that it suffices to choose $s$ and $m$ such that this parameter is small. Our result is a sparse analog of Gordon's theorem, which was concerned with a dense $\Phi$ having i.i.d. Gaussian entries. We qualitatively unify several results related to the Johnson-Lindenstrauss lemma, subspace embeddings, and Fourier-based restricted isometries. Our work also implies new results in using the sparse Johnson-Lindenstrauss transform in numerical linear algebra, classical and model-based compressed sensing, manifold learning, and constrained least squares problems such as the Lasso