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Traditional estimates of potential output based on the symmetric business cycle (boom–bust) view are prone to large retrospective revisions. The plucking view, which is supported by empirics, offers possible respite. Serious attempts to estimate the output ceiling in the plucking view, analogous to potential output in the traditional view, are scarce. This paper has three parts. The first estimates the output ceiling in a computationally simple approach. The second analyzes the relationship of the resultant output gap with inflation and with the unemployment rate. A comparison is made against output gap estimates based on prevailing methods. The third uses a vector autoregression (VAR) to analyze responses to supply and demand shocks. The paper finds that the plucking model offers three points of improvement over prevailing methods based on the boom–bust view. First, boom–bust estimates are prone to large retrospective revisions when two-sided filters are used, while the plucking estimates are not. Second, output gap estimates from both views do not correlate well with core inflation. This absence of evidence for a Phillips curve is problematic for the boom–bust view. The plucking estimates correlated well with the unemployment rate but the boom–bust estimates did not. Third, the output ceiling from the plucking model responded only to supply (oil price) shocks and not demand (interest rate) shocks, hence fits the description of a supply measure. This paper provides a template to estimate the output ceiling of the plucking model in other countries using publicly available macroeconomic data.

The application of the orthogonal complex AR model approach has been extended for the recognition of partially occluded objects. The 2-D boundary of an object is extracted and is divided into a number of line segments by locating the turning points. Each line segment is resampled into a fixed number of data points and a complex AR model is used to represent each line segment. An orthogonal estimator is implemented to determine the correct model order and to estimate the corresponding AR model parameters. Each line segment is associated with a minimum feature vector denoting the estimated AR model parameters and similar line segments for different patterns have similar AR model parameters. Recognition of an occluded object based on the matching of line segments of two patterns is derived. An algorithm for finding the turning points has also been devised, which is quite robust to various object sizes and orientation, resolution and noise effect of the object image. Experimental results were obtained to show the effectiveness of the proposed approach for the recognition of objects which are partly covered or partially occluded, and the approach is robust to different object sizes and orientation.

We consider an elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ, x, u), where (g(λ, x, s))/s → 0, as |s| → ∞. In [Arrieta et al., 2007, 2009] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work, we give conditions on the nonlinearity, guaranteeing the existence of a bifurcating branch which is neither subcritical nor supercritical, having an infinite number of turning points and an infinite number of resonant solutions.

We investigate the motion of a test particle in a d-dimensional, spherically symmetric and static spacetime supported by a mass M plus a Λ-term. The motion is strongly dependent on the sign of Λ. In Schwarzschild–de Sitter (SdS) space–time (Λ>0), besides the physical singularity at r=0 there are cases with two horizons and two turning points, one horizon and one turning point and the complete absence of horizon and turning points. For Schwarzschild–Anti de Sitter (SAdS) spacetime (Λ<0) the horizon coordinate is associated to an unique turning point.

The singularly perturbed problems with a turning point were discussed in [21]. The case where the limit problem is compatible with the given data was fully resolved. However, with limited compatibility conditions on the data, the asymptotic expansions were constructed only up to the order of the level of compatibilities. In this paper, using a smooth cut-off function compactly supported around the turning point we resolve the difficulties incurred from the non-compatible data and finally provide the full asymptotic expansions up to any order.

We consider the second-order linear differential equation