Comment on "Order parameter of A-like 3He phase in aerogel"

We argue that the inhomogeneous A-phase in aerogel is energetically more preferable than the "robust" phase suggested by I. A. Fomin, JETP Lett. 77, 240 (2003); cond-mat/0302117 and cond-mat/0401639.Comment: 2 page

Phonons in magnon superfluid and symmetry breaking field

Recent experiments [1],[2] which measured the spectrum of the Goldstone collective mode of coherently precessing state in 3He-B are discussed using the presentation of the coherent spin precession in terms of the Bose-Einstein condensation of magnons. The mass in the spectrum of the Goldstone boson -- phonon in the superfluid magnon liquid -- is induced by the symmetry breaking field, which is played by the RF magnetic fieldComment: 2 pages, JETP Letters style, no figures, version accepted in JETP Letter

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Assessment of load self-similarity properties in network structures

Main ratios allowing estimating the influence of self-similar load on the efficiency of network resource use have been obtained. It was shown that the degree of channel loading increases and buffer storage volume in switching nodes decreases in optimal case by minimum criterion of package delay average tim

NMR in Superfluid A-like Phase of 3^3He Confined in Globally Deformed Aerogel in Tilted Magnetic Field

NMR spectra in superfluid A-like phases confined in axially deformed aerogel in presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin precessing mode is rather narrow due to the U(1)LIM effect.Comment: 8 pages, 2 figure

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group