Some results concerning simple locally finite groups of 1-type

AbstractIn this paper several aspects of infinite simple locally finite groups of 1-type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1-type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1-type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depth…

Nanocluster di metalli preparati mediante ablazione Laser in liquido

Stationary states of a two-state defect quadratically coupled to a few bosonic modes

Abstract A fully quantistic microscopic two-phonon interaction model between an active centre and localized modes of an irradiated insulating material is introduced. Its exact diagonalization is accomplished with the help of a suitable unitary operator. Explicit expressions for the eigenvalues and eigenvectors are reported. The possible relevance of such a model in the context of the material science area is briefly pointed out.

Countable recognizability of primitive periodic finitary linear groups

Unipotent Finitary Linear Groups

Positive definite functions of finitary isometry groups over fields of odd characteristic

Abstract This paper is part of a programme to describe the lattice of all two-sided ideals in complex group algebras of simple locally finite groups. Here we determine the extremal normalized positive definite functions for finitary groups of isometries, defined over fields of odd characteristic.

The fragmentation of 5- and 3-substituted thiophene-2-carboxamides under electron impact

The 70 eV electron impact mass spectra of twelve 5- and 3-substituted thiophene-2-carboxamides are discussed with the aid of exact mass measurements and labelling experiments. All mass spectra exhibit pronounced molecular ions. Some isomeric 5- and 3-substituted title compounds can be differentiated by mass spectrometry. The fragmentation is influenced by a strong ‘ortho-effect’ which activates the NH3 elimination. In the other cases the most important fragmentation is NH2˙ loss, followed by CO elimination.

Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations

Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.

Irreducible finitary Lie algebras over fields of positive characteristic

A Lie subalgebra L of [gfr ][lfr ][ ](V) is said to be finitary if it consists of elements of finite rank. We study the situation when L acts irreducibly on the infinite-dimensional vector space V and show: if Char [ ] > 7, then L has a unique minimal ideal I. Moreover I is simple and L/I is solvable.

Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

Abstract A Lie subalgebraLof g l K (V) is said to befinitaryif it consists of elements of finite rank. We show that if Char  K  = 0, if dim K  Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple.

Structural and in situ vibrational study of luminescent cluster assembled silicon thin films

A Low Energy Cluster Beam Deposition apparatus is employed to produce cluster assembled silicon thin films (1-500 nm thick) by using a laser vaporization source. The generated clusters are studied since their formation through time of flight mass spectra and the calculated size in the gas phase are compared with those of the deposited aggregates obtained through Dynamic Scanning Force Microscopy. The deposited material is also studied "in situ" by Raman and infrared spectroscopy. The spectra reveal that the as deposited clusters are hydrogenated with negligible amount of oxide. A comparison of the film properties before and after their air exposure shows that the exposition induces a consis…

POSITIVE DEFINITE FUNCTIONS OF DIAGONAL LIMITS OF FINITE ALTERNATING GROUPS

The normalized positive definite class functions are determined for all those direct limits of finite alternating groups for which the embeddings are natural in the sense that every non-trivial -orbit in is natural.

Serial subalgebras of finitary Lie algebras

A Lie subalgebra L of glK(V ) is said to be finitary if it consists of elements of finite rank. We show that, if L acts irreducibly on V , and if V is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of L acts irreducibly on V too. When CharK 6= 2, it follows that the locally solvable radical of such L is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic 6= 2 are hyperabelian.

Effects of heat treatments on the properties of copper phthalocyanine films deposited by glow-discharge-induced sublimation

Copper phthalocyanine films have been deposited by glow-discharge-induced sublimation. The films have undergone postdeposition heat treatments in air at 250 and 290 °C for different times, ranging from 30 min to 14 h. The properties of as-deposited and heated films have been investigated by different techniques in order to determine the effects of heat treatments on the film properties. Fourier transform infrared analysis and UV−visible optical absorption analysis point out a gradual evolution of the film structure from a mixture of α and β polymorphs to the only β polymorph in the sample heated at 290 °C for 14 h. A pronounced decrease of carbon and nitrogen atomic percentages against an o…

Finitary Representations and Images of Transitive Finitary Permutation Groups

Abstract We characterize the point stabilizers and kernels of finitary permutation representations of infinite transitive groups of finitary permutations. Moreover, the number of such representations is determined.

Confined subgroups in periodic simple finitary linear groups

A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.

On the Interaction of Carbon Nanowires with Noble Metals through a Study of Their Surface-Enhanced Raman Spectra

This paper deals with the interaction of linear carbon chains (polyynes) with silver and gold surfaces in the form of nanometer-sized clusters. Surface-enhanced Raman signals have been detected rev...