Let p be a prime. We show that ZF + “Every countable set of p-element sets has an infinite partial choice function” is not strong enough to prove that every countable set of p-element sets has a choice function, answering an open question from [1]. The independence result is obtained by way of a permutation (FraenkelMostowski) model in which the set of atoms has the structure of a vector space ...

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 ⊕ 2. We also study proper interval orders and thei...

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as " infinite " , Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This gen...

The problem of High-Gain Observer Design is addressed for a class 3 × inhomogeneous linear hyperbolic systems with possibly distinct characteristic velocities and considering distributed measurement part the state. Applying an infinite-dimensional state transformation, system mapped into new set partial differential equations, satisfying appropriate form observer design. includes output correct...

We define the notion of a generic integral element for the Griffiths distribution on a weight two period domain, draw the analogy with the classical contact distribution, and then show how to explicitly construct an infinite-dimensional family of integral manifolds tangent to a given element.

We formulate and derive a generalization of an orthogonal rationalfunction basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to the infinite interval. By identifying the Fourier series as a biorthogonal composition of Jacobi polynomials/functions, we are able to define ge...

We say that a C∗-algebra A is approximately square root closed, if any normal element in A can be approximated by a square of a normal element in A. We study when A is approximately square root closed, and have an affirmative answer for AI-algebras, Goodearl type algebras over the torus, purely infinite simple unital C∗-algebras etc.