The expectation of a random variable is its average value, where each value is weighted according to the probability that it comes up. The expectation is also called the expected value or the mean of the random variable. For example, suppose we select a student uniformly at random from the class, and let R be the student’s quiz score. Then E [R] is just the class average —the first thing everyo...

We derive new estimates of the spectral dichotomy for matrices and matrix pencils which are based upon estimates of the restrictions of Green functions associated with the spectrum dichotomy problem onto the stable and unstable invariant subspaces and estimates of angles between these subspaces. De nouvelles estimations pour la dichotomie spectrale R esum e : Nous etablissons de nouvelles estim...

We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W ∈ H R and V ∈ T R are two Banach function spaces with the property that either W ∈ W R or V ∈ V R , then the admissibility of the pair W R, X , V R, X implies the existence of the exponential dichotomy...

Order Flow Patterns around Seasoned Equity Offerings and their Implications for Stock Price Movements In this study, we employ order imbalance measures to provide evidence that there exists an individual/institutional dichotomy in reactions to seasoned equity offerings (SEOs). The evidence supports the notion that small, possibly näıve, individual investors keep trading SEO stocks aggressively ...

We present several suucient conditions for exponential stability and di-chotomy of solutions of the evolution equation u 0 (t) = A(t)u(t) () on a Banach space X. Our main theorem says that if the operators A(t) generate analytic semigroups on X having exponential dichotomy with uniform constants and A() has a suuciently small HH older constant, then () has exponential dichotomy. We further stud...

[i] The hemispheric dichotomy is one the most fundamental and least understood features of Mars. The papers in this special section address aspects of the origin of the crustal dichotomy and the modification and evolution of the dichotomy boundary and the northern lowlands. These studies utilize new data from a variety of instruments on spacecraft operating in Mars orbit and on the surface. Thi...