We introduce a racing model with multiple product generations, product innovation, spin-outs, and licensing. Industry conditions and innovation characteristics affect who wins the race and who markets the resulting product. Small firms market their innovations when they pioneer a new generation or improve quality in a young generation and license their innovations in mature generations. If old ...

Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We wil...

tooth/implant supported fixed prostheses may present biomechanical design problems, as the implant is rigidly anchored within the alveolus, whereas the tooth is attached by the periodontal ligament to the bone allowing movement. many clinicians prefer tooth/implant supported fixed prosthesis designs with rigid connectors. however, there are some doubts about the effect of attachment placement i...

An ellipse rotating in the image plane can produce several different percepts. The two-dimensional (2D) percepts are either a rotating rigid ellipse or a constantly deforming non-rigid ellipse. The 3D percept is a rotating rigid circular disk that is tilted relative to the image plane. Stimuli that generate 3D percepts based on purely 2D rotational motion are known as stereokinetic stimuli. We ...

A common error, originally due to Ehrenfest, is corrected. Typeset using REVTEX 1 A recent book [1] with the same title as above contains 17 articles by various authors, following the English translation of a brief note by Paul Ehrenfest [2] who applied a Lorentz contraction to the rim of a rotating disk, whose radius was not contracted. This is plainly wrong: Lorentz contractions occur when we...

Nematic polymer networks (NPNs) are nematic elastomers within which the director is enslaved to elastic deformation. The free energy of a NPN sheet thickness $h$ has both stretching and bending components (the former scaling like h, latter $h^3$). sheets bear field $\mathbf{m}$ imprinted in them (usually, uniformly throughout their thickness); they can be activated by changing order (e.g. illum...

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ , or are weakly rigid. As a consequence we obtain tha...

This is a reply to Timothy Williamson’s paper ‘Tennant’s Troubles’. It defends against Williamson’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown...

This paper focuses on three research questions which are connected with combinations of modal logics: (i) Under which conditions can (frame-)completeness (and related properties) be transferred from a propositional modal logic (PML) to its quantificational counterpart (QML)? (ii) Does (frame-) completeness generally transfer from monomodal QMLs to their multimodal combination? (iii) Can complet...

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that ...