Volume 61, Issue 1

We prove some fundamental properties of monotone modal operators on bounded commutative integral residuated lattices (CRL). Moreover we give a positive answer to the problem left open in [RACHŮNEK, J.—ŠALOUNOV Á, D.: Modal operators on bounded commutative residuated Rℓ-monoids, Math. Slovaca 57 (2007), 321–332].

In the present paper we establish some new inequalities similar to extensions of Hilbert’s double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.

We consider compact Riemann surfaces Σg with genus at least 2. We explain the relation between the Reidemeister torsion of Σg and its period matrix.

In this paper, we obtain asymptotic bounds, under appropriate conditions, of solutions of third order difference equations of the form $$ \Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ), $$ where {p n} and {r n} are sequences of positive real numbers, and f, g: ℕ×ℝ2 → ℝ. Different forms of discrete Gronwall inequality are used to obtain these results.

Let A be an algebra and let X be an A-bimodule. A ∂-linear mapping d: A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ: A → X such that d(a 2) = ad(a)+δ(a)a for all a ∈ A. The main purpose of this paper is to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

We introduce an order relation in the set of modular biweights on a Banach C*-module X and give a description of this order relation in terms of representation associated with each modular biweight by GNS construction. We also characterize the extreme points in the set of all biweights φ defined on X such that φ(x 0, x 0) = λ 0. Furthermore, we discuss operator representations associated with modular biweights on Banach C*-modules.

Warped product manifolds are known to have applications in Physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [HONG, S. T.: Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B 120 (2005), 1227–1234]). The studies on warped product manifolds with extrinsic geometric point of view are intensified after B. Y. Chen’s work on CR-warped product submanifolds of Kaehler manifolds. Later on, similar studies are carried out in the setting of Sasakian manifolds by Hasegawa and Mihai. As Kenmotsu manifolds are themselves warped product spaces, it is interesting to investigate warped product submanifolds of Kenmotsu manifolds. In the present note a larger class of warped product submanifolds than the class of contact CR-warped product submanifolds is considered. More precisely the existence of warped product submanifolds of a Kenmotsu manifold with one of the factors an invariant submanifold is ensured, an example of such submanifolds is provided and a characterization for a contact CR-submanifold to be a contact CR-warped product submanifold is established.

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

We investigate lattices of retracts of monounary algebras. Semimodularity and concepts related to semimodularity (M-symmetry and Mac Lane’s condition) are dealt with. Further, we give a description of all connected monounary algebras with modular retract lattice.