The individual effects of dietary cholesterol and fat saturation on plasma lipoprotein concentrations were determined in an ethnically diverse population of normolipidemic young men (52 Caucasian, 32 non-Caucasian). The experimental diets contained approximately 200 or 600 mg/d of cholesterol, 36-38% of calories as fat, and high or low proportions of saturated and polyunsaturated fat (polyunsat...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus extending to non-algebraic lattices a result of L. Libkin. We illustrate this by various examples and counterexamples.

A set of vectors all of which have a constant (non-zero) norm value in an Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Réseaux et “designs” sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.

– We investigated different regimes of synchronization in large lattices of chaotic spiking-bursting neurons. The lattices exhibit the following features: developed spatio-temporal disorder with no synchronization; spatial clusters of bursting synchronization; homogeneous bursting synchronization; and complete chaotic synchronization. We observed a bistable synchronization phenomenon in a wide ...

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies heavily on the superrigidity theorem we propose in [Md], since we follow Margulis’ reduction of arithmeticity to superrigidity.

A notion of reticulation which provides topological properties on algebras has introduced on commutative rings in 1980 by Simmons in [5]. For a given commutative ring A, a pair (L, λ) of a bounded distributive lattice and a mapping λ : A → L satisfying some conditions is called a reticulation on A, and the map λ gives a homeomorphism between the topological space Spec(A) consisting of prime fil...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, typical passive exhibits single amplitude threshold marking onset of phenomenon, we show that inclusion feedback manifests additional thresholds depend upon specific boundary from which is stimulated, reali...