On the Equivalence of Dual Theories

We discuss the equivalence of two dual scalar field theories in 2 dimensions. The models are derived though the elimination of different fields in the same Freedman--Townsend model. It is shown that tree $S$-matrices of these models do not coincide. The 2-loop counterterms are calculated. It turns out that while one of these models is single-charged, the other theory is multi-charged. Thus the dual models considered are non-equivalent on classical and quantum levels. It indicates the possibility of the anomaly leading to non-equivalence of dual models.Comment: 14 pages, LaTeX; 2 figures, encapsulated PostScrip

On Groups whose Contranormal Subgroups are Normally Complemented

2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained

Linear groups with the maximal condition on subgroups of infinite central dimension

Let A a vector space over a field F and let H be a subgroup of GL(F, A). We define centdimF H to be dimF (A/CA (H)). We say that H has finite central dimension if centdimF H is finite and we say that H has infinite central dimension otherwise. We consider soluble linear groups, in which the (ordered by inclusion) set of all subgroups having infinite central dimension satisfies the maximal condition

The influence of arrangement of subgroups on the group structure

Investigation of groups satisfying certain related to arrangement of subgroups conditions allows algebraists to introduce and describe many important classes of groups. Most of these conditions are based on the fundamental notion of normality and built with the help of this concept di erent subgroup chains (series). Some of important results obtained on this way we will discuss in the current surve

Abnormal subgroups and Carter subgroups in some infinite groups

Some properties of abnormal subgroups in generalized soluble groups will be considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it will be proven that a subgroup H of a radical group G is abnormal in G if and only if every intermediate subgroup for H coincides with its normalizer in G. This result will extend on radical groups the well-known criterion of abnormality for finite soluble groups obtained by D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugations will be also proven

On the relationships between the factors of upper and lower central series in groups and other algebraic structures

We discuss some new recent development of the well known classical R. Baer and B. Neumann theorems. More precisely, we want to show the thematic which evolved from the mentioned classical results describing the relations between the central factor-group and the derived subgroup in an in nite group. We track these topics not only in groups, but also in some other algebraic structure

Magnetic properties of ferrofluid emulsions: The effect of droplet elongation

The paper is concerned with a theoretical explanation of the experimentally observed effect of non-monotonic field dependence of the effective magnetic permeability of ferrofluid emulsion. In a weak magnetic field, the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Thus, the emulsion magnetic permeability increases in weak magnetic fields. Further strengthening of the external magnetic field cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Hence, the effective magnetic permeability of the ferrofluid emulsion starts decreasing. The developed theoretical model describes well the experimental observations

Adsorption-desorption kinetics in nanoscopically confined oligomer films under shear

The method of molecular dynamics computer simulations is employed to study oligomer melts confined in ultra-thin films and subjected to shear. The focus is on the self-diffusion of oligomers near attractive surfaces and on their desorption, together with the effects of increasing energy of adsorption and shear. It is found that the mobility of the oligomers near an attractive surface is strongly decreased. Moreover, although shearing the system forces the chains to stretch parallel to the surfaces and thus increase the energy of adsorption per chain, flow also promotes desorption. The study of chain desorption kinetics reveals the molecular processes responsible for the enhancement of desorption under shear. They involve sequences of conformations starting with a desorbed tail and proceeding in a very fast, correlated, segment-by-segment manner to the desorption of the oligomers from the surfaces.