Stream biofilms are exposed to dynamic conditions of flow velocity and organic carbon availability. Thus, the aim of this study was to investigate the response of biofilms formed with and without humic substances (HSs) to an increase in flow velocity (0.04-0.10 ms(-1)) and HSs concentration (9.7+/-1.0 to 19.8+/-0.4 mgL(-1) C). The highest amount of biofilm, measured as volatile suspended solids...

Within the categoryW of archimedean lattice-ordered groups with weak order unit, we show that the objects of the form C (L), the set of continuous real-valued functions on a locale L, are precisely those which are divisible and complete with respect to a variant of uniform convergence, here termed indicated uniform convergence. We construct the corresponding completion of aW-object A purely alg...

A relaxed notion of category is presented having in mind the categorical caracterization of the mechanisms for combining probabilistic automata, since the composition of the appropriate morphisms is not always deened. A detailed discussion of the required notion of morphism is provided. The partiality of composition of such morphisms is illustrated at the abstract level of countable probability...

We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups Fn. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operat...

A partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show tha...

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptoti...

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other rel...

We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum. Our approach is based on the Rudolph-Weiss result on the equality of conditional entropies for actions of countable amenable groups with the same orbits. Relative completely positive entropy actions are also considered. An application to the entropic pr...

We prove that in the category of achimedean lattice-ordered groups with weak unit there is no homomorphism-closed monoreflection strictly between the strongest essential monoreflection (the so-called “closure under countable composition”) and the strongest monoreflection (the epicompletion). It follows that in the category of regular σframes, the only non-trivial monoreflective subcategory that...

We say that a countable linear ordering L is countably complementable if there exists a linear ordering L, possibly uncountable, such that for any countable linear ordering B, L does not embed into B if and only if B embeds into L. We characterize the linear orderings which are countably complementable. We also show that this property is equivalent to the countable version of the finitely faith...