It is well established in literature that the public debt and economic growth bear positive and non-linear relationship. However, in recent literature, evidence of no causal relationship is found when accounted for endogeneity in case of advanced economies (Panizza & Presbitero, 2014). Chudik, Mohaddes, Pesaran, & Raissi, (2017) analyse the data on forty countries and find no evidence of universally applicable threshold effect in the relationship between debt and growth. These advancements in the debt-growth literature provides the motivation to re-explore the relationship between public debt and economic growth under non-linearity and endogeneity in context of developing economies of South Asia including Pakistan, India, Bangladesh and Sri-Lanka for the period 1980-2014. There exists a significant, positive but nonlinear relationship between the public debt and economic growth for the selected set of developing countries when accounted for endogeneity and non-linearity. The negative association between the public debt and economic growth for SAARC region is found when the debt level is higher than 61% of GDP which is quite lower than developed economies (90% of GDP). Individual threshold levels for debt-to-GDP ratio divulge that Sri Lanka, Pakistan and India need to control their public borrowings as their current debt levels are higher and/or around the respective threshold levels.

This study investigates uranium solvent extraction under AMEX process conditions. The use of pure extractants without diluents or phase modifiers allows not only to reduce the use of volatile organic compounds, but also to provide higher extraction yields without third phase formation. Pure extractants are protonated amines or quaternary ammoniums with suitable counter ion, which act at the interface between ion pairs and protic ionic liquids. The mixture of sulfates anion (SO42-) and bis(trifluoromethanesulfonyl)imide anion (NTf2-) revealed unexpected nonlinear extraction behaviors, which appear highly important to rationalize for optimized application. Spectroscopic analysis (NMR, UV-vis, FT-IR, and EXAFS) showed that uranium extraction occurs via protonated amine and three sulphates. Nonlinear extraction could further be interpreted by considering water and acid transfer between the two phases: at lower sulphate ratios, the release of acid from the organic phase into the aqueous phase was shown to influence the number of protonated amines in the organic phase, affecting uranium extraction before its enhancement. Furthermore, the extraction loss at higher sulphate ratios, was assigned to the destabilization of bidentate uranium-sulphate complexes due to a competition between water and sulphates.

Negative feedback to the back gate of MOS devices available in FD-SOI technologies can be used to improve linearity of operational amplifiers. Two operational amplifiers designed and fabricated in a 22nm FD-SOI technology illustrate this technique, its advantages and limitations.

Mediterranean catchments are characterized by significant spatial and temporal hydrological variability caused by the interaction of natural as well human-induced abiotic and biotic factors. This study investigates the (non-)linearity rainfall-runoff relationship at multiple temporal scales in representative small Mediterranean catchments (i.e., < 10 km2) to achieve a better understanding of the hydrological response. Rainfall-runoff relationship was evaluated in 44 catchments at annual and event –203 events in 12 of these 44 catchments– scales. A linear rainfall-runoff relation was observed at annual scale with higher scatter in pervious than impervious catchments. Larger scattering was observed at event scale, although pervious lithology and agricultural land use promoted significant rainfall-runoff linear relations in winter and spring. These relationships were particularly analysed during five hydrological years in Es Fangar catchment (3.35 km2; Mallorca, Spain) as a temporal downscaling to assess intra-annual variability in which antecedent wetness conditions played a significant role in runoff generation.

Observed sea surface Ka-band normalized radar backscatter cross section (NRCS) and Doppler velocity (DV) exhibit energy at low frequencies (LF) below the surface wave range. It is shown that non-linearity in NRCS-wave slope Modulation Transfer Function (MTF) and inherent NRCS averaging within the footprint account for the NRCS and DV LF variance with the exception of VV NRCS for which almost half of the LF variance is attributable to wind fluctuations. Although the distribution of radar DV is quasi-Gaussian suggesting virtually little impact of non-linearity, the LF DV variations arise due to footprint averaging of correlated local DV and non-linear NRCS. Numerical simulations demonstrate that MTF non-linearity weakly affects traditional linear MTF estimate (less than 10% for |MTF|< 20). Thus the linear MTF is a good approximation to evaluate the DV averaged over large footprints typical of satellite observations.

The problem of fluid dynamics can be greatly simplified if, for every point in space, the strain-rate tensor is diagonalized. This tensor is introduced into the Navier-Stokes equations via material law and divergence of the stress tensor. This article shows that local SO(3)xU(1) gauge fields can be used to locally diagonalize the diffusion components of the strain-rate tensor. The gauge fields resulting from the connection can be interpreted as convection components of the flow, they show properties of quasiparticles and can be interpreted as elementary vortices. Thus, the proposed approach not only offers new insights for the solution and situative simplification of the Navier-Stokes equations, it also uncovers hidden symmetries within the flow convection, allowing - depending on boundary conditions - further interpretation.

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. It allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. Using Hamilton’s principle we transform the differential equation relativistically into an integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by the rotations of real particle field geometries in Minkowski space. Because the properties of energy are universal the same equations are then used to describe the field geometry of galaxies despite vast differences in lifetime. They reveal a symmetry between the electromagnetic fields of atoms and the gravitational fields of galaxies due to similarities in the exchange of energy by radial and transverse fields. Our analysis reveals that the conjugate variables energy and time permit differences between atomic and galactic structure to be compared in a more intuitive way than by means of the differential equations of motion which use the conjugate variables position and momentum.

Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals. Comparison with measured results.

The epistemology of the traditional risk assessment examined has a taxonomy based upon deterministic, behaviouristic and compatibilist methodologies which are likely driven by neo-liberal market related requirements for bigger, faster cheaper wind-turbines. Analysis of available risk assessments suggested that there is no conscious effort to deceive the reader although the intended audience is unclear. The language, and scoring mechanisms utilized indicates the presence of conformity bias, confirmation bias, and numerical inconsistency leading to data ossification. By reverse engineering risk assessment content, Pragmatic and Social Psychological aspects can be investigated, and the adequacy of the document can be evaluated using evidence-based models.

In synthetic diamond plate, the intrapulse correlated dynamics of self-phase modulation and spontaneous Raman scattering by optical phonons were for the first time directly investigated for tightly focused (focusing numerical aperture NA = 0.25) positively-chirped visible-range ultrashort laser pulses with variable durations (0.3-9.5 ps) and energies, transmitted through the sample. The observed modulation of the transmitted light spectra and Stokes Raman scattering spectra for the different pulse durations were related to nonthermal excitation of nonlinear phonon polarization and its eventual picosecond-scale suppression due to thermal decay of optical phonons on the timescale of electron-phonon thermalization in the material.