Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity. These analogies presented together with their Lagrangian Hamiltonian formulations an invariant sequence.

We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify local diffusivity tensor and also interactions between become important. provide a simple general formula effective diffusion constant along as well first non-trivial finite time correction arbitrary flows channel, interaction potentials expressi...

A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$­1,m­1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...

Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the quotient of some group by its center) by a condition on the size of the factors in the invariant factor decomposition (the group must be noncyclic and the top two invariant factors must be equal). We provide a different characterization, given in terms of a condition on the lattice of subgroups. Name...

Throughout this paper, all groups are finite. A group class closed under taking homomorphic images and finite subdirect products is called a formation . The symbol σ denotes some partition of the set primes. V. G. Safonov, I. N. Safonova, A. Skiba (Commun. Algebra. 2020. Vol. 48, № 9. P. 4002–4012) defined generalized σ-function. Any function f form : È {Ø} → {formations groups}, where (Ø) ≠ ∅,...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers. The product bases of that group are represented by the multiplicative group of invertible elements in that matrix ring. All products in the Baer-Specker group are characterized, and a lemma of László Fuchs regarding such products i...