Let$X$be a smooth$n$-dimensional projective variety embedded in some projective space ℙ^{$N$}over the field ℂ of the complex numbers. Associated with the general projection of$X$to a space ℙ^{$N$-$m$}($N$-$m$>$n$+1) one defines an extended Gauss map $\overline{\gamma}\colon\overline{X}\rightarrow\text{Gr}(n;N-m)$ (in case$N$-$m$>2$n$-1 this is the Gauss map of the image of$X$under the projection). We prove that $\overline{X}$ is smooth. In case any two different points of$X$do have disjoint tangent spaces then we prove that $\overline{\gamma}$ is injective.

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This article analyses the effect of cognitive behavioral therapy (CBT) for individuals with mild or moderate mental illness. We study the effects on sick leave, health care consumption, and drug prescriptions. We find that CBT improved health and prevented sick leave for individuals who were not on sick leave when treatment was initiated but had no effect for individuals who were on sick leave when the treatment was initiated.