We show that volume-preserving perturbations of some product actions of property (T) groups exhibit a “foliation rigidity” property, which reduces the partially hyperbolic action to a family of hyperbolic actions. This is used to show that certain partially hyperbolic actions are locally rigid.

For each group G having an infinite normal subgroup with the relative property (T) (e.g. G = H ×K, with H infinite with property (T) and K arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G) × Λ. We deduce that G has uncountably many non stabl...

The present study examined the hypothesis that Asian cultures’ dialectical way of thinking influences emotion reports. A dialectical way of thinking sees emotions of the opposite valence (e.g., happy, sad) as compatible with each other. In contrast, Western philosophy considers these emotions to be in conflict with each other. We examined correlations between frequency estimates of pleasant emo...

Let (X, ν) be a probability space and suppose a free group Fm withm generators acts on (X, ν) by measure-preserving transformations. Let {a1, . . . , am} be a set of free generators for Fm and let T1, . . . , Tm : X → X be transformations corresponding to the generators. Write T−i = T −1 i for i = 1, . . . ,m, and set A = {−m, . . . ,−1, 1, . . . ,m}. We also have the action Fm on L1(X, ν), def...

The uniform norm of the differential of the n-th iteration of a diffeomorphism is called the growth sequence of the diffeomorphism. In this paper we show that there is no lower universal growth bound for volume preserving diffeomorphisms on manifolds with an effective T2 action by constructing a set of volume-preserving diffeomorphisms with arbitrarily slow growth.

A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0, ∞) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.

After reviewing some notions of the formal theory of diierential equations we discuss the completion of a given system to an involutive one. As applications to symmetry theory we study the eeects of local solvability and of gauge symmetries, respectively. We consider non-classical symmetry reductions and more general reductions using diierential constraints.

We introduce the notion of ∧and ∨-pairs of functions on lattices as an abstraction of the notions of metric and its related entropy for probability distributions. This approach allows us to highlight the relationships that exist between various properties of metrics and entropies and opens the possibility of extending these concepts to other algebraic structures.

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G)×Λ. We deduce that ...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ on the probability space such that the 1’st cohomology group of σΛ, H (σΛ), is equal to Char(G)×Λ. We deduce that G has un...