Finding All Solutions of Equations in Free Groups and Monoids with Involution

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented emph{recompression} technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk at CSR 2014 in Moscow, June 7 - 11, 201

Polarization studies of Rotating Radio Transients

We study the polarization properties of 22 known rotating radio transients (RRATs) with the 64-m Parkes radio telescope and present the Faraday rotation measures (RMs) for the 17 with linearly polarized flux exceeding the off-pulse noise by 3$\sigma$. Each RM was estimated using a brute-force search over trial RMs that spanned the maximum measurable range $\pm1.18 \times 10^5 \, \mathrm{rad \, m^2}$ (in steps of 1 $\mathrm{rad \, m^2}$), followed by an iterative refinement algorithm. The measured RRAT RMs are in the range |RM| $\sim 1$ to $\sim 950$ rad m$^{-2}$ with an average linear polarization fraction of $\sim 40$ per cent. Individual single pulses are observed to be up to 100 per cent linearly polarized. The RMs of the RRATs and the corresponding inferred average magnetic fields (parallel to the line-of-sight and weighted by the free electron density) are observed to be consistent with the Galactic plane pulsar population. Faraday rotation analyses are typically performed on accumulated pulsar data, for which hundreds to thousands of pulses have been integrated, rather than on individual pulses. Therefore, we verified the iterative refinement algorithm by performing Monte Carlo simulations of artificial single pulses over a wide range of S/N and RM. At and above a S/N of 17 in linearly polarized flux, the iterative refinement recovers the simulated RM value 100 per cent of the time with a typical mean uncertainty of $\sim5$ rad m$^{-2}$. The method described and validated here has also been successfully used to determine reliable RMs of several fast radio bursts (FRBs) discovered at Parkes.Comment: Submitted to MNRAS, 10 pages, 6 figure

Investigation of octupole vibrational states in 150Nd via inelastic proton scattering (p,p'g)

Octupole vibrational states were studied in the nucleus $^{150}\mathrm{Nd}$ via inelastic proton scattering with \unit[10.9]{MeV} protons which are an excellent probe to excite natural parity states. For the first time in $^{150}\mathrm{Nd}$, both the scattered protons and the $\gamma$ rays were detected in coincidence giving the possibility to measure branching ratios in detail. Using the coincidence technique, the $B(E1)$ ratios of the decaying transitions for 10 octupole vibrational states and other negative-parity states to the yrast band were determined and compared to the Alaga rule. The positive and negative-parity states revealed by this experiment are compared with Interacting Boson Approximation (IBA) calculations performed in the (spdf) boson space. The calculations are found to be in good agreement with the experimental data, both for positive and negative-parity states

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201

Distinction between the Poole-Frenkel and tunneling models of electric field-stimulated carrier emission from deep levels in semiconductors

The enhancement of the emission rate of charge carriers from deep-level defects in electric field is routinely used to determine the charge state of the defects. However, only a limited number of defects can be satisfactorily described by the Poole-Frenkel theory. An electric field dependence different from that expected from the Poole-Frenkel theory has been repeatedly reported in the literature, and no unambiguous identification of the charge state of the defect could be made. In this article, the electric field dependencies of emission of carriers from DX centers in AlxGa1-xAs:Te, Cu pairs in silicon, and Ge:Hg have been studied applying static and terahertz electric fields, and analyzed by using the models of Poole-Frenkel and phonon assisted tunneling. It is shown that phonon assisted tunneling and Poole-Frenkel emission are two competitive mechanisms of enhancement of emission of carriers, and their relative contribution is determined by the charge state of the defect and by the electric-field strength. At high-electric field strengths carrier emission is dominated by tunneling independently of the charge state of the impurity. For neutral impurities, where Poole-Frenkel lowering of the emission barrier does not occur, the phonon assisted tunneling model describes well the experimental data also in the low-field region. For charged impurities the transition from phonon assisted tunneling at high fields to Poole-Frenkel effect at low fields can be traced back. It is suggested that the Poole-Frenkel and tunneling models can be distinguished by plotting logarithm of the emission rate against the square root or against the square of the electric field, respectively. This analysis enables one to unambiguously determine the charge state of a deep-level defect

Diode area melting single-layer parametric analysis of 316L stainless steel powder

Diode area melting (DAM) is a novel additive manufacturing process that utilises customised architectural arrays of low power laser diode emitters for high speed parallel processing of metallic powdered feedstock. The laser diodes operate at shorter laser wavelengths (808 nm) than conventional SLM fibre lasers (1064 nm) theoretically enabling more efficient energy absorption for specific materials. This investigation presents a parametric analysis of the DAM process, identifying the effect of powder characteristics, laser beam profile, laser power and scan speed on the porosity of a single-layer sample. Also presented is the effect of process energy density on melt pool depth (irradiated thermal energy penetration capable of achieving melting) on 316L stainless steel powder. An analysis of the density and the melt depth fraction of single layers is presented in order to identify the conditions that lead to the fabrication of fully dense DAM parts. Energy densities in excess of 86 J/mm3 were theorised as sufficient to enable processing of fully dense layers

Mixed-symmetry octupole and hexadecapole excitations in N=52 isotones

In addition to the well-established quadrupole mixed-symmetry states, octupole and hexadecapole excitations with mixed-symmetry character have been recently proposed for the N = 52 isotones 92Zr and 94Mo. We performed two inelastic proton-scattering experiments to study this kind of excitations in the heaviest stable N = 52 isotone 96Ru. From the combined experimental data of both experiments absolute transition strengths were extracted

Continuous flow micro-cell for electrochemical addressing of engineered bio-molecules

Abstract A micro-cell consisting of a planar array of Au working electrodes, covered by a glass reservoir (600 nl capacity), connected with perpendicular capillaries and provided with an Ag/AgCl wire reference electrode (RE) has been manufactured. Addressed on-chip immobilization and sensing of biomolecules was demonstrated by the immobilization of histidine (HIS) tagged alkaline phosphatase (AP) under continuous flow (10 l/min) conditions on the base of electrochemically deposited multilayer (EDM) of cysteamine modified by nitrilotriacetic acid (NTA). The presented method allows the immobilization of different biomolecules on the ready-to-use reservoir covered chip without needs of manual biomolecule deposition. Further on, the detection of analytes can be performed using the electrochemical measurements. Since the methods of biomolecule deposition and sensing are both electrochemical, this allows simplifying the production technology using cheaper detection instruments compared to prevailing present-day optical detection modes