The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example have been correcte

Carboplatin binding to a model protein in non-NaCl conditions to eliminate partial conversion to cisplatin, and the use of different criteria to choose the resolution limit

Hen egg white lysozyme (HEWL) co-crystallisation conditions of carboplatin without sodium chloride (NaCl) have been utilised to eliminate partial conversion of carboplatin to cisplatin observed previously. Tetragonal HEWL crystals were successfully obtained in 65% MPD with 0.1M citric acid buffer at pH 4.0 including DMSO. The X-ray diffraction data resolution to be used for the model refinement was reviewed using several topical criteria together. The CC1/2 criterion implemented in XDS led to data being significant to 2.0{\AA}, compared to the data only being able to be processed to 3.0{\AA} using the Bruker software package (SAINT). Then using paired protein model refinements and DPI values based on the FreeR value, the resolution limit was fine tuned to be 2.3{\AA}. Interestingly this was compared with results from the EVAL software package which gave a resolution limit of 2.2{\AA} solely using crossing 2, but 2.8{\AA} based on the Rmerge values (60%). The structural results showed that carboplatin bound to only the N{\delta} binding site of His-15 one week after crystal growth, whereas five weeks after crystal growth, two molecules of carboplatin are bound to the His-15 residue. In summary several new results have emerged: - firstly non-NaCl conditions showed a carboplatin molecule bound to His-15 of HEWL; secondly binding of one molecule of carboplatin was seen after one week of crystal growth and two molecules were bound after five weeks of crystal growth; and thirdly the use of several criteria to determine the diffraction resolution limit led to the successful use of data to higher resolution.Comment: 14 pages; submitted to Acta Cryst D Biological Crystallography reference number tz504

Detection of neutral hydrogen in early-type dwarf galaxies of the Sculptor Group

We present our results of deep 21 cm line (HI) observations of five early and mixed-type dwarf galaxies in the nearby Sculptor group using the ATNF 64m Parkes Radio Telescope. Four of these objects, ESO294-G010, ESO410-G005, ESO540-G030, and ESO540-G032, were detected in HI with neutral hydrogen masses in the range of 2-9x10^5 M_{\odot} ($M_{HI}/L_{B}$ = 0.08, 0.13, 0.16, and 0.18, respectively). These HI masses are consistent with the gas mass expected from stellar outflows over a large period of time. Higher resolution radio data from the Australia Telescope Compact Array were further analysed to measure more accurate positions and the distribution of the HI gas. In the cases of dwarfs ESO294-G010 and ESO540-G030, we find significant offsets of 290 pc and 460 pc, respectively, between the position of the HI peak flux and the center of the stellar component. These offsets are likely to have internal cause such as the winds from star-forming regions. The fifth object, the spatially isolated dwarf elliptical Scl-dE1, remains undetected at our 3\sigma limit of 22.5 mJy km/s and thus must contain less than 10^5 M_{\odot} of neutral hydrogen. This leaves Scl-dE1 as the only Sculptor group galaxy known where no interstellar medium has been found to date. The object joins a list of similar systems including the Local Group dwarfs Tucana and Cetus that do not fit into the global picture of the morphology-density relation where gas-rich dwarf irregulars are in relative isolation and gas-deficient dwarf ellipticals are satellites of more luminous galaxies.Comment: 21 pages, 4 figures, to be published in AJ (accepted

Structure and electronic properties of the quasi-one-dimensional Ba₂Co₁₋ₓZnₓS₃ series

This work focuses on the structure and physical properties of the solid solution Ba₂Co₁₋ₓZnₓS₃ (0 ≤ x ≤ 1), a family of quasi-one-dimensional sulfides with end members Ba₂CoS₃ and Ba₂ZnS₃. The structure of selected compounds with increasing Zn²⁺ content has been analysed using, neutron diffraction, TEM and EXAFS and the physical properties via magnetic susceptibility and resistivity measurements. The progressive substitution of the non-magnetic Zn²⁺ cation for Co²⁺ rapidly destroys the antiferromagnetic transition present at 46 K in the quasi one-dimensional Ba₂CoS₃, leading to paramagnetic behaviour down to the lowest investigated temperature (5K) for compounds with x > 0.25. For compounds with x ≥ 0.4, a pure CW regime is recovered around 300 K, yielding effective moments consistent with the g factor of the tetrahedrally coordinated Co²⁺ previously determined for Ba₂CoS₃. The Zn²⁺/Co²⁺ substitution also removes the metallic-like behaviour of Ba₂CoS₃ causing an increase in the value of the resistivity with all the Ba₂Co₁₋ₓZnₓS₃ compounds showing semiconducting behaviour. The negative magnetoresistance of Ba₂CoS₃ is improved by the Zn²⁺/Co²⁺ substitution, with values of – 6% for Ba₂Co₀.₇₅Zn₀.₂₅S₃, – 9% for Ba₂Co₀.₅Zn₀.₅S₃ and – 8% for Ba₂Co₀.₂₅Zn₀.₇₅S₃. However, there does not seem to be a correlation between the values of the resistivity and the magnetoresistance and the content of Zn²⁺, leading to the hypothesis that transport properties may be linked more closely to extrinsic properties

Weak commutation relations of unbounded operators: nonlinear extensions

We continue our analysis of the consequences of the commutation relation [S,T]=\Id, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations

Flow optimization study of a batch microfluidics PET tracer synthesizing device.

We present numerical modeling and experimental studies of flow optimization inside a batch microfluidic micro-reactor used for synthesis of human-scale doses of Positron Emission Tomography (PET) tracers. Novel techniques are used for mixing within, and eluting liquid out of, the coin-shaped reaction chamber. Numerical solutions of the general incompressible Navier Stokes equations along with time-dependent elution scalar field equation for the three dimensional coin-shaped geometry were obtained and validated using fluorescence imaging analysis techniques. Utilizing the approach presented in this work, we were able to identify optimized geometrical and operational conditions for the micro-reactor in the absence of radioactive material commonly used in PET related tracer production platforms as well as evaluate the designed and fabricated micro-reactor using numerical and experimental validations

Single-molecule Studies Of p53 Sliding Along DNA

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Weyl formulas for annular ray-splitting billiards

We consider the distribution of eigenvalues for the wave equation in annular (electromagnetic or acoustic) ray-splitting billiards. These systems are interesting in that the derivation of the associated smoothed spectral counting function can be considered as a canonical problem. This is achieved by extending a formalism developed by Berry and Howls for ordinary (without ray-splitting) billiards. Our results are confirmed by numerical computations and permit us to infer a set of rules useful in order to obtain Weyl formulas for more general ray-splitting billiards

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here