Self-Similar Tilings of Fractal Blow-Ups

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic

Range-only Target Localisation using Geometrically Constrained Optimisation

The problem of optimal range-only localisation of a single target is of considerable interest in two-dimensional search radar networking. For coping with this problem, a range-only target localisation method using synchronous measurements from radars is presented in the real ellipsoidal earth model. In the relevant radar localisation scenario, geometric relationships between the target and three radars were formed. A set of localisation equations was derived on range error in such a scenario. Using these equations, the localisation task has been formulated as a nonlinear weighted least squares problem that can be performed using the Levenberg- Marquardt (LM) algorithm to provide the optimal estimate of the target’s position. To avoid the double value solutions and to accelerate the convergence speed for the LM algorithm, the initial value was approximately given according to observations from two radars. In addition, the relative validity has been defined to evaluate the performance of the proposed method. The performance of the proposed approach is evaluated using two simulation experiments and a real-test experiment, and it has been found to possess higher localisation accuracy than the other conventional method.Defence Science Journal, Vol. 65, No. 1, January 2015, pp.70-76, DOI:http://dx.doi.org/10.14429/dsj.65.547

{μ-6,6′-Dimeth­oxy-2,2′-[cyclo­hexane-1,2-diylbis(nitrilo­methyl­idyne)]diphenolato}methanol-μ-nitrato-dinitratocopper(II)europium(III)

In the title dinuclear salen-type complex, [CuEu(C22H24N2O4)(NO3)3(CH3OH)], the CuII ion is five-coordinated to two imine N atoms and two phenolate O atoms and one O from the bridging nitrate group. The EuIII ion is ligated to three nitrate groups, four O atoms from the salen-type ligand and one methanol mol­ecule, leading to a distorted tenfold coordination for the rare earth cation. One of the three nitrate anions is disordered over two positions in a 0.66 (5):0.34 (5) ratio

A γ\gamma-ray Quasi-Periodic modulation in the Blazar PKS 0301−-243?

We report a nominally high-confidence $\gamma$-ray quasi-periodic modulation in the blazar PKS 0301$-$243. For this target, we analyze its \emph{Fermi}-LAT Pass 8 data covering from 2008 August to 2017 May. Two techniques, i.e., the maximum likelihood optimization and the exposure-weighted aperture photometry, are used to build the $\gamma$-ray light curves. Then both the Lomb-Scargle Periodogram and the Weighted Wavelet Z-transform are applied to the light curves to search for period signals. A quasi-periodicity with a period of $2.1\pm0.3$ yr appears at the significance level of $\sim5\sigma$, although it should be noted that this putative quasi-period variability is seen in a data set barely four times longer. We speculate that this $\gamma$-ray quasi-periodic modulation might be evidence of a binary supermassive black hole.Comment: 9 pages, 8 figures; Accepted for publication in Ap