Applications of Commutator-Type Operators to pp-Groups

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly $p^m$ fixed points such that $\phi^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with $(p,n,m,k)$-bounded index in G. We also establish its analogue for Lie p-rings. The proofs make use of the theory of commutator-type operators.Comment: 11 page

Different sensing mechanisms in single wire and mat carbon nanotubes chemical sensors

Chemical sensing properties of single wire and mat form sensor structures fabricated from the same carbon nanotube (CNT) materials have been compared. Sensing properties of CNT sensors were evaluated upon electrical response in the presence of five vapours as acetone, acetic acid, ethanol, toluene, and water. Diverse behaviour of single wire CNT sensors was found, while the mat structures showed similar response for all the applied vapours. This indicates that the sensing mechanism of random CNT networks cannot be interpreted as a simple summation of the constituting individual CNT effects, but is associated to another robust phenomenon, localized presumably at CNT-CNT junctions, must be supposed.Comment: 12 pages, 5 figures,Applied Physics A: Materials Science and Processing 201

Small amplitude quasi-breathers and oscillons

Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in $D$ spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, $D_{crit}=4$, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.Comment: 24 pages, 19 figure

Ellipsoidal shapes in general relativity: general definitions and an application

A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary, axisymmetric perfect-fluid spacetimes with a so-called confocal inside ellipsoidal symmetry are investigated in detail under the assumption that the 4-velocity of the fluid is parallel to a time-like Killing vector field. A class of perfect-fluid metrics representing interior NUT-spacetimes is obtained along with a vacuum solution with a non-zero cosmological constant.Comment: Latex, 22 pages, Revised version accepted in Class. Quantum. Grav., references adde

Stringy Robinson-Trautman Solutions

A class of solutions of the low energy string theory in four dimensions is studied. This class admits a geodesic, shear-free null congruence which is non-twisting but in general diverging and the corresponding solutions in Einstein's theory form the Robinson-Trautman family together with a subset of the Kundt's class. The Robinson-Trautman conditions are found to be frame invariant in string theory. The Lorentz Chern-Simons three form of the stringy Robinson-Trautman solutions is shown to be always closed. The stringy generalizations of the vacuum Robinson-Trautman equation are obtained and three subclasses of solutions are identified. One of these subclasses exists, among all the dilatonic theories, only in Einstein's theory and in string theory. Several known solutions including the dilatonic black holes, the pp- waves, the stringy C-metric and certain solutions which correspond to exact conformal field theories are shown to be particular members of the stringy Robinson-Trautman family. Some new solutions which are static or asymptotically flat and radiating are also presented. The radiating solutions have a positive Bondi mass. One of these radiating solutions has the property that it settles down smoothly to a black hole state at late retarded times.Comment: Latex, 30 Pages, 1 Figure; to appear in Phys. Rev.

Towards a critical theory of communication as renewal and update of Marxist humanism in the age of digital capitalism

This paper's task is to outline some foundations of a critical, Marxist-humanist theory of communication in the age of digital capitalism. It theorises the role of communication in society, communication and alienation, communication in social struggles, social struggles for democratic communication, the contradictions of digital capitalism, and struggles for digital socialist humanism. Marxist humanism is a counter-narrative, counter-theory, and counter-politics to neoliberalism, new authoritarianism, and postmodernism. A critical theory of communication can should draw on this intellectual tradition. Communication and work stand in a dialectical relationship. Communication mediates, organises and is the process of the production of sociality and therefore of the reproduction of society. Society and communication are in class and capitalist societies shaped by the antagonism between instrumental and co-operative reason. Authoritarianism and humanism are two basic, antagonistic modes of organisation of society and communication. Instrumental reason creates and universalises alienation. Digital capitalism is a dimension of contemporary society where digital technologies such as the computer, the Internet, the mobile phone, tablets, robots, and AI-driven (“smart”) technologies mediate the accumulation of capital, influence, and reputation. A Marxist-humanist theory of communication aims to inform struggles for a good, commons-based, public Internet in a good, commons-based society that has a vivid, democratic public sphere

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page