Contour deformation trick in hybrid NLIE

The hybrid NLIE of AdS_5 x S^5 is applied to a wider class of states. We find that the Konishi state of the orbifold AdS_5 x (S^5/Z_S) satisfies A_1 NLIE with the source terms which are derived from contour deformation trick. For general states, we construct a deformed contour with which the contour deformation trick yields the correct source terms.Comment: 39 pages, 6 figures, v2: discussion on analyticity constraints replaced by consistent deformed contou

Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.Comment: numerical results adde

Hybrid-NLIE for the AdS/CFT spectral problem

Hybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its gamma-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a few appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. The integral equations are written explicitly for the ground state of the gamma-deformed system. We linearize these NLIE equations, analytically calculate the first correction to the asymptotic solution and find agreement with analogous results coming from the original TBA formalism. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.Comment: 63 pages, 1 figur

Konishi operator at intermediate coupling

TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not vanis

Barriers to the development of palliative care in Western Europe

The Eurobarometer Survey of the <i>EAPC Task Force on the Development of Palliative Care in Europe</i> is part of a programme of work to produce comprehensive information on the provision of palliative care across Europe. Aim: To identify barriers to the development of palliative care in Western Europe. Method: A qualitative survey was undertaken amongst boards of national associations, eliciting opinions on opportunities for, and barriers to, palliative care development. By July 2006, 44/52 (85%) European countries had responded to the survey; we report here on the results from 22/25 (88%) countries in Western Europe. Analysis: Data from the Eurobarometer survey were analysed thematically by geographical region and by the degree of development of palliative care in each country. Results: From the data contained within the Eurobarometer, we identified six significant barriers to the development of palliative care in Western Europe: (i) Lack of palliative care education and training programmes (ii) Lack of awareness and recognition of palliative care (iii) Limited availability of/knowledge about opioid analgesics (iv) Limited funding (v) Lack of coordination amongst services (vi) Uneven palliative care coverage. Conclusion: Findings from the EAPC Eurobarometer survey suggest that barriers to the development of palliative care in Western Europe may differ substantially from each other in both their scope and context and that some may be considered to be of greater significance than others. A number of common barriers to the development of the discipline do exist and much work still remains to be done in the identified areas. This paper provides a road map of which barriers need to be addressed

Mathematics education and technology

Recent international surveys such as the Organisation for Economic Co-operation and Development (OECD) report Students, Computers and Learning ( 2015) highlight the wide gap in students’ access to, and use of, technology in secondary mathematics in participating countries. The OECD “snapshot” methodology in which 15-year-old students were asked if they (or their teachers) had performed a range of mathematical tasks using computers in the month preceding their completion of the Programme for International Student Assessment (PISA) survey revealed low levels of technology use (see Fig. 1)

Exploring the mirror TBA

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.Comment: 69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published versio

Extensive Spectroscopy and Photometry of the Type IIP Supernova 2013ej

We present extensive optical ($UBVRI$, $g'r'i'z'$, and open CCD) and near-infrared ($ZYJH$) photometry for the very nearby Type IIP SN ~2013ej extending from +1 to +461 days after shock breakout, estimated to be MJD $56496.9\pm0.3$. Substantial time series ultraviolet and optical spectroscopy obtained from +8 to +135 days are also presented. Considering well-observed SNe IIP from the literature, we derive $UBVRIJHK$ bolometric calibrations from $UBVRI$ and unfiltered measurements that potentially reach 2\% precision with a $B-V$ color-dependent correction. We observe moderately strong Si II $\lambda6355$ as early as +8 days. The photospheric velocity ($v_{\rm ph}$) is determined by modeling the spectra in the vicinity of Fe II $\lambda5169$ whenever observed, and interpolating at photometric epochs based on a semianalytic method. This gives $v_{\rm ph} = 4500\pm500$ km s$^{-1}$ at +50 days. We also observe spectral homogeneity of ultraviolet spectra at +10--12 days for SNe IIP, while variations are evident a week after explosion. Using the expanding photosphere method, from combined analysis of SN 2013ej and SN 2002ap, we estimate the distance to the host galaxy to be $9.0_{-0.6}^{+0.4}$ Mpc, consistent with distance estimates from other methods. Photometric and spectroscopic analysis during the plateau phase, which we estimated to be $94\pm7$ days long, yields an explosion energy of $0.9\pm0.3\times10^{51}$ ergs, a final pre-explosion progenitor mass of $15.2\pm4.2$~M$_\odot$ and a radius of $250\pm70$~R$_\odot$. We observe a broken exponential profile beyond +120 days, with a break point at +$183\pm16$ days. Measurements beyond this break time yield a $^{56}$Ni mass of $0.013\pm0.001$~M$_\odot$.Comment: 29 pages, 23 figures, 15 tables, Published in The Astrophisical Journa