Search results for " 05"
showing 10 items of 51 documents
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Pre- and syn-eruptive geochemistry of volcanic gases from Soufriere Hills of Montserrat, West Indies
1998
International audience; Soufriere Hills fumaroles contained magmaderived volatiles before and during the eruption initiated in 1995 but also preserved a typical and quite steady hydrothermal coinposition. Chemical changes due to increased boiling and a greater input of oxidizing magmatic gas occurred only at Galway's Soufriere, the most active fumarolic field. Hydrothermal buffering of the fumaroles has been favoured by their remote location (!-2 km) froin the eruptive vents and by a preferential degassing of the uprising magma through intrusive conduits under the crater. High temperature (720øC) gas collected froin the extruding lava dome in Feb. 1996 was chemically and isotopically repres…
GRB 050904 at redshift 6.3: observations of the oldest cosmic explosion after the Big Bang
2005
We present optical and near-infrared observations of the afterglow of the gamma-ray burst GRB 050904. We derive a photometric redshift z = 6.3, estimated from the presence of the Lyman break falling between the I and J filters. This is by far the most distant GRB known to date. Its isotropic-equivalent energy is 3.4x10^53 erg in the rest-frame 110-1100 keV energy band. Despite the high redshift, both the prompt and the afterglow emission are not peculiar with respect to other GRBs. We find a break in the J-band light curve at t_b = 2.6 +- 1.0 d (observer frame). If we assume this is the jet break, we derive a beaming-corrected energy E_gamma = (4-12)x10^51 erg. This limit shows that GRB 050…
Packing colorings of subcubic outerplanar graphs
2018
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,\ldots,k)$-packing coloring of a graph $G$ is called the packing chromatic number of $G$, denoted $\chi_{\rho}(G)$. The question of boundedness of the packing chromatic number in the class of subcubic (planar) graphs was investigated in several earlier papers; recently it was established that the invariant is unbounded in the class of all sub…
Polar bosons in one-dimensional disordered optical lattices
2013
We analyze the effects of disorder and quasi-disorder on the ground-state properties of ultra-cold polar bosons in optical lattices. We show that the interplay between disorder and inter-site interactions leads to rich phase diagrams. A uniform disorder leads to a Haldane-insulator phase with finite parity order, whereas the density-wave phase becomes a Bose-glass at very weak disorder. For quasi-disorder, the Haldane insulator connects with a gapped generalized incommesurate density wave without an intermediate critical region.
Linear and cyclic radio k-labelings of trees
2007
International audience; Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that |f(x)−f(y)| ≥ k+1−dG(x,y), for any two distinct vertices x and y, where dG(x,y) is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling. The linear (cyclic, respectively) radio k-labeling number of G is the minimum span of a linear (cyclic, respectively) radio k-labeling of G. In this p…
The pre-outburst flare of the A 0535+26 August/September 2005 outburst
2008
We study the spectral and temporal behavior of the High Mass X-ray Binary A 0535+26 during a `pre-outburst flare' which took place ~5 d before the peak of a normal (type I) outburst in August/September 2005. We compare the studied behavior with that observed during the outburst. We analyse RXTE observations that monitored A 0535+26 during the outburst. We complete spectral and timing analyses of the data. We study the evolution of the pulse period, present energy-dependent pulse profiles both at the initial pre-outburst flare and close to outburst maximum, and measure how the cyclotron resonance-scattering feature (hereafter CRSF) evolves. We present three main results: a constant period P=…
Splittings of Toric Ideals
2019
Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.
Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras
2012
The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.
$(BV,L^p)$-decomposition, $p=1,2$, of Functions in Metric Random Walk Spaces
2019
In this paper we study the $(BV,L^p)$-decomposition, $p=1,2$, of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the case $p=1$ we also study the associated geometric problem and the thresholding parameters.