On the growth function of direct decompositions associated with homology of free abelianized extensions

AbstractLet G be an arbitrary group given by a free presentation G=F/N. We deal with the homology group Hn(Ф, Z) where Ф = F/[N, N]. It is known that if G has no p-torsion then the p-component of Hn(Ф, Z) (p odd) has a natural direct decomposition of the form ⊕kHnk(G,ZpZ). The number of direct summands is a function of dimension n. We prove that this function grows faster than ns for any s but slower than an for any a>1. Indeed a more precise asymptotic estimate is given. We also study maximal multiplicity of the group H∗(G, ZpZ) in the above decomposition and get information on decomposition of two other periodic groups related to Hn(Ф,Z)

Spin-Isospin Excitations and Muon Capture by Nuclei

By analyzing the energy-weighted moments of the strength function calculated in RPA and beyond it is shown that the explanation of the effect of missing strength of Gamow-Teller transitions requires that residual interaction produce high-excited $1^{+}$ particle-hole collective states. The example of this interaction is presented. The manifestations of spin-isospin nuclear response in nuclear muon capture are discussed.Comment: 16 pages, 5 figures, 2 tables. The talk at the XVI International School on Nuclear Physics, Neutron Physics and Nuclear Energy, September 19-26, Varna, Bulgari

Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors

We show the possibility of long-range ferrimagnetic ordering with a saturation magnetisation of the order of 1 Bohr magneton per spin for arbitrarily low concentration of magnetic impurities in semiconductors, provided that the impurities form a superstructure satisfying the conditions of the Lieb-Mattis theorem. Explicit examples of such superstructures are given for the wurtzite lattice, and the temperature of ferrimagnetic transition is estimated from a high-temperature expansion. Exact diagonalization studies show that small fragments of the structure exhibit enhanced magnetic response and isotropic superparamagnetism at low temperatures. A quantum transition in a high magnetic field is considered and similar superstructures in cubic semiconductors are discussed as well.Comment: 6 pages,4 figure

Conformal symmetric model of the porous media

AbstractWe present a conformal theory for the random fractal fields. As an example, the density of the porous matter is considered. The equation that expresses density in terms of a nonfractal field is evaluated. Assuming the hypothesis of scale and conformal symmetry for the latter, we derive the correlation functions for density. The log-normal conformal model is studied

Groups with non-central dimension quotients

AbstractLet G be a group and let Dn(G) and γn(G) be its nth dimension and nth lower central subgroups. In an earlier paper we proved that Dn(G)γn(G) is abelian. Here we prove that Dn(G)γn(G) is not, in general, central in Gγn(G). In fact, for any s there exists a group G and an integer n such that Dn(G)γn(G) is not contained in the sth upper central subgroups of Gγn(G)

Crystal-field-induced magnetostrictions in the spin reorientation process of Nd2_2Fe14_{14}B-type compounds

Volume expansion $\Delta V / V$ associated with the spin reorientation process of Nd$_2$Fe$_{14}$B-type compounds has been investigated in terms of simple crystalline-electric-field (CEF) model. In this system, $\Delta V / V$ is shown to be a direct measure of second order CEF energy. Calculated anomalies in $\Delta V / V$ associated with the first-order magnetization process of Nd$_2$Fe$_{14}$B are presented, which well reproduced the observations.Comment: 2 pages, 2 figures, to appear in J. Magn. Magn. Mate