On the trivial units in finite commutative group rings

Let G be a finite abelian group and F a finite field. A criterion is found for all units in the group ringFG to be trivial. This attainment is also extended to the general case for arbitrary abelian groups and fields

On the socles of characteristic subgroups of Abelian p-groups

Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained

Commutative Weakly Invo–Clean Group Rings

A ring R is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring R and each abelian group G, we find only in terms of R, G and their sections a necessary and sufficient condition when the group ring R[G] is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings

Rings Additively Generated by Periodic Elements

In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major cases, additively periodic rings remain periodic too; this includes, for instance, algebraic algebras, group rings, and matrix rings over commutative rings. Moreover, we also obtain some independent results for the new class of rings; for example, the triangular matrix rings retain that property.Comment: 16 page

Non-universal size dependence of the free energy of confined systems near criticality

The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric $\phi^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $\Lambda$ causes a non-universal leading size dependence $f_s \sim \Lambda^{d-2} L^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.Comment: RevTex, 4 page

Out-of-equilibrium properties of the semi-infinite kinetic spherical model

We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and the scaling functions of two-time surface correlation and response functions are determined explicitly in the dynamical scaling regime. In the low-temperature phase our results show that for the case of Dirichlet boundary conditions the value of the non-equilibrium surface exponent $b_1$ differs from the usual bulk value of systems undergoing phase ordering.Comment: 22 pages, 4 figures included, submitted to J. Phys.

Fluctuation - induced forces in critical fluids

The current knowledge about fluctuation - induced long - ranged forces is summarized. Reference is made in particular to fluids near critical points, for which some new insight has been obtained recently. Where appropiate, results of analytic theory are compared with computer simulations and experiments.Comment: Topical review, 24 pages RevTeX, 6 figure

Exact Three Dimensional Casimir Force Amplitude, CC-function and Binder's Cumulant Ratio: Spherical Model Results

The three dimensional mean spherical model on a hypercubic lattice with a film geometry $L\times \infty ^2$ under periodic boundary conditions is considered in the presence of an external magnetic field $H$. The universal Casimir amplitude $\Delta$ and the Binder's cumulant ratio $B$ are calculated exactly and found to be $\Delta =-2\zeta (3)/(5\pi)\approx -0.153051$ and $B=2\pi /(\sqrt{5}\ln ^3[(1+\sqrt{5})/2]).$ A discussion on the relations between the finite temperature $C$-function, usually defined for quantum systems, and the excess free energy (due to the finite-size contributions to the free energy of the system) scaling function is presented. It is demonstrated that the $C$-function of the model equals 4/5 at the bulk critical temperature $T_c$. It is analytically shown that the excess free energy is a monotonically increasing function of the temperature $T$ and of the magnetic field $|H|$ in the vicinity of $T_c.$ This property is supposed to hold for any classical $d$-dimensional $O(n),n>2,$ model with a film geometry under periodic boundary conditions when $d\leq 3$. An analytical evidence is also presented to confirm that the Casimir force in the system is negative both below and in the vicinity of the bulk critical temperature $T_c.$Comment: 12 pages revtex, one eps figure, submitted to Phys. Rev E A set of references added with the text needed to incorporate them. Small changes in the title and in the abstrac

First g(2+) measurement on neutron-rich 72 Zn, and the high-velocity transient field technique for radioactive heavy-ion beams

The high-velocity transient-field (HVTF) technique was used to measure the g factor of the 2+ state of 72Zn produced as a radioactive beam. The transient-field strength was probed at high velocity in ferromagnetic iron and gadolinium hosts using 76Ge beams. The potential of the HVTF method is demonstrated and the difficulties that need to be overcome for a reliable use of the TF technique with high-Z, high-velocity radioactive beams are revealed. The polarization of K-shell vacancies at high velocity, which shows more than an order of magnitude difference between Z = 20 and Z = 30 is discussed. The g-factor measurement hints at the theoretically predicted transition in the structure of the Zn isotopes near N = 40