Let ${\cal S}$ be a Scott set, or even an ω-model of WWKL. Then for each A ε S, either there is X ε S that is weakly 2-random relative to A, or there is X ε S that is 1-generic relative to A. It follows that if A1,…,An ε S are noncomputable, there is X ε S such that each Ai is Turing incomparable with X, answering a question of Kučera and Slaman. More generally, any ∀∃ sentence in the language of partial orders that holds in ${\cal D}$ also holds in ${{\cal D}^{\cal S}}$, where ${{\cal D}^{\cal S}}$ is the partial order of Turing degrees of elements of ${\cal S}$.

This study investigates the role of transfer from the stronger language by focusing on the interpretation of definite articles in Spanish and English by Spanish heritage speakers (i.e., minority language-speaking bilinguals) residing in the U.S., where English is the majority language. Spanish plural NPs with definite articles can express generic reference (Los elefantes tienen colmillos de marfil), or specific reference (Los elefantes de este zoológico son marrones). English plurals with definite articles can only have specific reference (The elephants in this zoo are brown), while generic reference is expressed with bare plural NPs (Elephants have ivory tusks). Furthermore, the Spanish definite article is preferred in inalienable possession constructions (Pedro levantó la mano “Peter raised the hand”), whereas in English the use of a definite article typically means that the body part belongs to somebody else (alienable possession). Twenty-three adult Spanish heritage speakers completed three tasks in Spanish (acceptability judgment, truth-value judgment, and picture–sentence matching tasks) and the same three tasks in English. Results show that the Spanish heritage speakers exhibited transfer from English into Spanish with the interpretation of definite articles in generic but not in inalienable possession contexts. Implications of this finding for the field of heritage language research and for theories of article semantics are discussed.

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties.The work is motivated by two applications: an existence result for the problem of maximizing the rate of exponential decay of a damped membrane and an approximate controllability result for the bilinear Schrödinger equation.

While the classification project for the simple groups of finite Morley rank is unlikely to produce a classification of the simple groups of finite Morley rank, the enterprise has already arrived at a considerably closer approximation to that ideal goal than could have been realistically anticipated, with a mix of results of several flavors, some classificatory and others more structural, which can be combined when the stars are suitably aligned to produce results at a level of generality which, in parallel areas of group theory, would normally require either some additional geometric structure, or an explicit classification. And Bruno Poizat is generally awesome, though sometimes he goes too far.

The significance of singularities in the design and control of robot manipulators is well known, and there is an extensive literature on the determination and analysis of singularities for a wide variety of serial and parallel manipulators—indeed such an analysis is an essential part of manipulator design. Singularity theory provides methodologies for a deeper analysis with the aim of classifying singularities, providing local models and local and global invariants. This paper surveys applications of singularity-theoretic methods in robot kinematics and presents some new results.

For smooth or real-analytic single-input, control-affine, non-linear systems, with at least two ouputs, observability for any input ofa given class is generic. This class can be either the class of inputs bounded with their derivatives up to a certain order, or the class ofpolynomial inputs with bounded degree.