If the vertices of a triangle are projected onto a given line, the perpendiculars from the projections to the corresponding sidelines of the triangle intersect at one point, the orthopole of the line with respect to the triangle. We prove several theorems on orthopoles using the Pappus theorem, a fundamental result of projective geometry.

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E∆ S2m−1 ([0, R)) are uniformly bounded as an operator from H(S) to L(S) for all p ∈ (1,∞). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on R × R. Suppose that L is a positive definite, self-adjoint operator acting on L(X,μ), where X is a me...

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that ...

Nonlinear partial differential equations are defined as fibred submanifolds of a jet bundle. The definitions of prolongation and symbol are given and given interpretations. Projections, formal properties, and linearisation are also discussed. Almost no attempt is made to maintain notational consistency with the standard literature.

This article studies the role of working conditions and health for elderly female day-care teachers' decision to enter early retirement. Entry into retirement is analysed in a duration framework that allows for unobserved heterogeneity in the baseline hazard. Data are from a Danish longitudinal data set based on administrative register records for 1997-2006. Working conditions are measured by f...

In this paper we introduce new robust estimators for the logistic and probit regressions for binary, multinomial, nominal and ordinal data and apply these models to estimate the parameters when outliers or inluential observations are present. Maximum likelihood estimates don't behave well when outliers or inluential observations are present. One remedy is to remove inluential observations from ...

The problem of the generation of homogeneous grids for spherical domains is considered in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obt...

In the framework of a geographic application displaying maps, there are several solutions for protecting a sensitive object. Sensitive objects can be hidden, masked, blurred or even replaced by fake objects. In this paper we suggest a framework to specify protection mechanisms to enforce whenever a prohibition is derived from the security policy. This framework includes (i) logical rules allowi...

Kinetic transition networks can now be calculated for small proteins using geometry optimisation to characterise minima, transition states and pathways, and unimolecular rate theory to supply rate constants corresponding to each transition state. The networks can be visualised by constructing disconnectivity graphs, revealing striking differences between good structure-seeking systems and a mod...

Correctly assessing the consequences of events is essential for a successful interaction with the world. It not only requires a causal understanding of the world but also the ability to distinguish whether a given event is the result of an agent’s own action (intervention) or simply the consequence of the world being in action (observation). Previous studies have shown that humans can learn cau...