aSchool of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China; bCollege of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, People’s Republic of China; cKey Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, People’s Republic...

This paper is concerned with a class of continuoustime uncertain systems which satisfy a certain Integral Quadratic Constraint. The problems of robust filtering, robust prediction, and robust smoothing for such systems are defined, and nonconservative solutions are given in terms of Riccati differential equations. This paper also addresses a problem of robust observability for this class of unc...

We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors T. C —» D between small categories with finite limits for which the functor /*: LEX(D,Set) —> LEX...

Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise nonisomorphic finitely generated, non-recursively-presentable groups. These are the first examples of such residually finite groups.

For a number of locally finitely presentable categories K we describe the codensity monad full embedding all objects into K. We introduce concept D-ultrafilter on an object, where D is “nice” cogenerator prove that assigns to every object representing D-ultrafilters it. Our result covers e.g. sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.

We say that L is weakly η-like if L/∼ is isomorphic to the natural ordering of rational numbers. We construct a computable presentation of any low weakly η-like linear ordering with no strongly η-like interval. Also we prove that there exists a noncomputably presentable low2 weakly η-like linear ordering with no strongly η-like interval.