The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
The family Pλ of absolutely continuous probabilities w.r.t. the σ-finite measure λ is equipped with a structure of an infinite dimensional Riemannian manifold modeled on a real Hilbert. Firstly, the relation between the Hellinger distance and the Fischer metric is analysed on the positive cone Mλ+ of bounded measures absolutely continuous w.r.t. λ, appearing as a flat Riemannian manifold. Secondly, the statistical manifold Pλ is seen as a submanifold of Mλ+ and Amari-Chensov α-connections are derived. Some α-self-parallel curves are explicitely exhibited.
Addressing collisions between environmental protection and competing economic and social interests often constitutes the very core of environmental cases. At the constitutional level, a balancing approach based on the doctrine of proportionality is frequently employed to resolve contradictions between conflicting values. In this article, I demonstrate how the proportionality doctrine in its traditional meaning can be applied to balancing interests in environmental cases. Then I bring to the forefront two innovative ways of engaging proportionality in the environmental protection; one employing proportionality as an interpretative instrument with the power to help determining the scope and content of the right to environment; and the other adjusting proportionality to the form of eco-proportionality, offering a restructured framework to rule the human-nature relationship., Hana Müllerová., and Obsahuje bibliografické odkazy
Let $C(X,\mathbb Z )$, $C(X,\mathbb Q )$ and $C(X)$ denote the $\ell $-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$, respectively. Characterizations are given for the extensions $C(X,\mathbb Z )\leq C(X,\mathbb Q )\leq C(X)$ to be rigid, major, and dense.
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
A ring extension $R\subseteq S$ is said to be FO if it has only finitely many intermediate rings. $R\subseteq S$ is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension $R\subseteq S$ to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair with only finitely many intermediate rings. We also obtain as a corollary several new and old characterizations of Prüfer and integral domains satisfying the corresponding finiteness conditions.
Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.