The Cauchy-Schlomilch transformation

The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given

Validation of Faecal NIRS for Monitoring the Diet of Confined and Grazing Goats

Goats are used for brush control and ecological management of Mediterranean grazing lands. Farmers are willing to cooperate with communities but they need an easy method to evaluate the daily intake of nutrients. A calibration of the chemical attributes of goats\u27 diets was set-up, based on faecal near infrared (NIR) spectra (Landau et al., 2004; Table 1). The accuracy of this methodology was estimated by using the standard error of cross-validation (SECV), which represents the variability in the difference between predicted and reference values when the equation is applied sequentially to subsets of data from the calibration data set. This procedure is justified in situations with calibration samples that are randomly selected from a natural population, but may give over-optimistic results, in particular if data are replicated. The standard error of prediction (SEP) represents the variability in the difference between predicted and reference values when the equation is applied to an external (i.e., not used in any step of the calibration) validation data set. (Naes et al., 2002). The aim of the present study was to test the robustness of predicting dietary CP, in vitro dry matter digestibility (IVDMD), and NDF percentages in goats\u27 diets, using faecal samples totally external to calibrations

Custom Integrated Circuits

Contains report on one research project.U.S. Air Force - Office of Scientific Research (Contract F49620-80-C-0073

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $\phi^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP 20-11-9

Point vortices on the sphere: a case with opposite vorticities

We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.Comment: 35 pages, 9 figure

The structural and dynamic responses of Stange Ice Shelf to recent environmental change

Stange Ice Shelf is the most south-westerly ice shelf on the Antarctic Peninsula, a region where positive trends in atmospheric and oceanic temperatures have been recently documented. In this paper, we use a range of remotely sensed datasets to evaluate the structural and dynamic responses of Stange Ice Shelf to these environmental changes. Ice shelf extent and surface structures were examined at regular intervals from optical and radar satellite imagery between 1973 and 2011. Surface speeds were estimated in 1989, 2004 and 2010 by tracking surface features in successive satellite images. Surface elevation change was estimated using radar altimetry data acquired between 1992 and 2008 by the European Remote Sensing Satellite (ERS) -1, -2 and Envisat. The mean number of surface melt days was estimated using the intensity of backscatter from Envisat’s Advanced Synthetic Aperture Radar instrument between 2006 and 2012. These results show significant shear fracturing in the southern portion of the ice shelf linked to enhanced flow speed as a consequence of measured thinning. However, we conclude that, despite the observed changes, Stange Ice Shelf is currently stable

On the K^+D Interaction at Low Energies

The Kd reactions are considered in the impulse approximation with NN final-state interactions (NN FSI) taken into account. The realistic parameters for the KN phase shifts are used. The "quasi-elastic" energy region, in which the elementary KN interaction is predominantly elastic, is considered. The theoretical predictions are compared with the data on the K^+d->K^+pn, K^+d->K^0pp, K^+d->K^+d and K^+d total cross sections. The NN FSI effect in the reaction K^+d->K^+pn has been found to be large. The predictions for the Kd cross sections are also given for slow kaons, produced from phi(1020) decays, as the functions of the isoscalar KN scattering length a_0. These predictions can be used to extract the value of a_0 from the data.Comment: 22 pages, 5 figure

Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling

The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general geometry of the form $L^{d-d'}\times\infty^{d'}\times L_{\tau}^{z}$ ( $L$-linear space size and $L_{\tau}$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\leq d'\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.Comment: 33pages, revtex+epsf, 3ps figures included submitted to PR

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating