Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Electron Transport in Configurational Model of Ferromagnetic Fulleride with Triple Orbital Degeneracy

Abstract

Phenomenon of ferromagnetic ordering was for a long time associated exclusively with transition metal and rare-earth compounds. Nowadays this view is challenged by growing evidence that in molecular carbon-based systems the ferromagnetic alignment of spins can be observed as well. We have developed a microscopical model of a fulleride electronic subsystem taking into account triple orbital degeneracy of energy states within the configurational-operator approach. Using the Green function method the energy spectrum of the model has been calculated. Conditions for the ferromagnetic state stabilization have been determined. Static electrical conductivity and effective masses of current carriers in the system with orbitally degenerated energy band have been obtained. In the ground state and for low temperatures at different forms of unperturbed density of electronic states the concentration dependences of transport characteristics for less-then-half-filled lower quasiparticle subband have been calculated.     

Monotony by some Newton-like methods

The article treats the monotone behaviour of successive approximations computed by some Newton-like method for solving a nonlinear operator equation in a Banach space endowed with a partial ordering for which it is a Banach lattice.     

Membrane switch hypothesis. 1. Cell density influences lateral domain structure of tumor cell membranes

The domain structure of human cancer cells membranes was investigated by electron paramagnetic resonance (EPR) in different phases of cell growth, and the results were compared to those obtained for nonmalignant cells. On the basis of computer simulation of the EPR spectra using a newly developed GHOST condensation routine it was suggested that plasma membranes of cancer cells have less lateral lipid domain types at confluent conditions than in the exponential growing phase, while in nonmalignant cells the domain structure does not change significantly during cell growth. In accordance to our experimental data we propose a membrane switch hypothesis: disappearance of certain membrane domain types might act as a switch promoting the clustering of membrane constituents into the active units in a common lipid membrane domain and thus influencing the physiology of cells.     

Lattices on simplicial partitions

In this paper, (d+1)-pencil lattices on simplicial partitions in R^d are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of this fact leads to an efficient computer algorithm for the design of a lattice.     

The structure of irreducible matrix groups with submultiplicative spectrum

We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p ²× p ² matrices if p is an odd prime.     

Magnetooptical bistability of a layered semiconductor in the region of exciton absorption

The effect of weak external magnetic fields on the conditions for implementing optical bistability in the region of exciton absorption of layered semiconductors has been theoretically investigated. By the example of the 2H polytype of lead diiodide, it is shown that, changing the strength of an external magnetic field, one can form conditions for implementing bistability and effectively control the position and sizes of the hysteresis loop of exciton absorption.