On the embedding of core-free projective images of normal subgroups

Sunto Siano G e due gruppi, : GG una proiettività e N un sottogruppo normale di G. Vengono provati alcuni risultati sulle proprietà di immersions in e G rispettivamente, del gruppi , la chiusura normale di N in modulo il nocciolo di N in , e .

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Supported by a C.N.R. grant.     

On some properties of the metric subalgebras ofℓ ∞

The objects studied are the subalgebras of which contain c_o. These are isometrically isomorphic to the algebras C( ) where is a compactification of a discrete denumerable set N . It is shown: 1) If is metric then there is a projection of norm 1, P: C( ) C( ) with kernel c_o defined by PF = f o where is a retraction of onto = – N . 2) If is metric, then the group of homeomorphisms of is isomorphic to a complete group of permutations of the natural numbers . 3) The group of homeomorphisms of a compact metric space is the homomorphic image of a complete group of permutations of ("complete" means "no outer automorphisms, trivial center").     

Embeddings of anisotropic Sobolev spaces on unbounded domains

Summary Integral representations of junctions in the anisotropic Sobolev spaces on unbounded domains are used in the study of the embeddings of these spaces into Lebesgue spaces. Estimates of entropy numbers of the embedding are obtained, where k, p and q satisfy certain conditions and where is a certain type of quasibounded domain,     

Infimal generators and dualities between complete lattices

Summary We give some applications of infimal generators of complete lattices, in the sense of Kutateladze and Rubinov [12], to the study of dualities between two complete lattices E and F (i.e., mappings : E F satisfying for all and all index sets I, including the empty set I=Ø). We give some additional results for E=(2^X, ), F=(2^W, ) and E=(¯R^X, ), F=(¯R^W, ) (where X and W are arbitrary sets), with suitable families of infimal generators. We obtain some lattice- theoretic properties of the relations of [22] between dualities : (2^X, ) (2^W, ), binary relations X×W, polarities (): (2^X, ) (2^W, ), coupling functionals : X×W ¯R and Fenchel-Moreau conjugations c():(¯R^X, ) (¯R^W,).     

A fitting class construction

Summary We present a Fitting Class construction which exploits the properties of a certain class of finite soluble groups of nilpotent length three, called -groups in the paper. In addition we look at a wider class of groups, called in the paper, also of nilpotent length three and examine the question as to what -groups are in .A number of examples are given to illuminate the various classes.The author would like to thank HermannHeineken for supervising his dissertation, from which this paper has sprung, the German Academic Exchange Service (DAAD) for enabling him to study with Prof. Heineken at Universität Würzburg and An Roinn Oideachais for the fellowship which is at present supporting him at University College, Galway.     

Natural operations with projectable tangent valued forms on a fibred manifold

Summary Let p: EB be a fibred manifold. Then, we consider the sheaf (E)=(B)P(E) of (local) projectable tangent valued forms on E, where (B) is the sheaf of (local) differential forms on B andP(E) is the sheaf of (local) projectable vector fields on E. The Frölicher-Nijenhuis bracket makes (E) to be a sheaf of graded Lie algebras [18]. In this paper we study all natural R -bilinear operations on (E) which are of Frölicher-Nijenhuis type. By using the analytical method of [16], we prove that there is a three-parameter family of such operators on (E). As a consequence, we obtain a result on the unicity of the covariant differential of tangent valued forms and of the curvature associated with a given connection on E. All manifolds and mappings are assumed to be infinitely differentiable.This paper has been written during the author's visit at the Institute of Applied Mathematics «Giovanni Sansone». Florence, Italy. The author would like to thank ProfessorMarco Modugno for his kind hospitality and for stimulating discussions.     

Isometrische Immersionen der Kodimension 2 von Raumformen

Let M, resp. , denote Riemannian manifolds of dimensions m>4, resp. =m+2, and of constant sectional curvatures C, resp. , with 0 and is a standard space form, then the foliation L is a (globally) trivial fibre bundle with fibre S^m–1.     

Topological and bornological characterisations of ideals in von Neumann algebras: I

Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces.     

Completion of an additive measure to a σ-additive measure by an extension of the space

For an algebra of subsets of a set X there is constructed a set and an algebra of its subsets so that the mapping is a one-to-one correspondence between and and for each additive measure on the measure on defined by the equation is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written.     

Spherical elastic-plastic waves

Zusammenfassung Es wird die Fortpflanzung elastisch-plastischer Spannungswellen in einem unendlichen Medium betrachtet, welches einer idealen Spannungs-Verformungs-Kurve folgt, Trescas Fliesskriterium unterworfen ist und einen sphärischen Hohlraum enthält, wobei an der Fläche des Hohlraumes ein Stoss angenommen wird. Ein rechnerisches Verfahren, basiert auf endliche Differenzen, wird entwickelt and ein Beispiel gegeben.

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Notation radial stress - tangential stress - K yield stress - _rr non-dimensional radial stress ( /K) - non-dimensional tangential stress ( /K) - , Lame's constants - K _b Bulk constant (=(3+2)/3) - v Poisson's constant - Material density - C Elastic wave velocity (=((+2)/)^1/2) - C _p Plastic wave velocity (=(K _b /)^1/2) - distance from center of cavity - r ₀ cavity radius - v non-dimensional radial co-ordinate (= /r ₀) - time - t non-dimensional time (=C /r ₀) - radial displacement - u non-dimensional radial displacement (=/r ₀) - particle velocity - v non-dimensional particle velocity (= /C) - pressure - P(t) non-dimensional pressure (= /K)     

Un théorème de Vitali-Hahn-Saks pour les semimartingales

Summary Let (, , P) be a complete probability space; let _t0 be an increasing right-continuous family of -complete sub--fields of ; let be a sequence of semimartingales. Assume that for all positive t and for all bounded predictable processes H, the r.v.'s converge in probability to a limit J(t, H) when n tends to infinity. Then there exists a semimartingale X such that, for all t and H, J(t, H)= .     

Lightlike periodic trajectories in space-times

Let ., _z be a Lorentz metric on a manifold such that isnot compact. We prove the existence of infinitely many lightlike periodic trajectories in by using variational methods and Ljusternik-Schnirelman theory.Sponsored by M.U.R.S.T. (fondi 60% «Problemi differenziali nonlineari e teoria dei punti critici»; fondi 40% «Equazioni differenziali e calcolo delle variazioni»).     

Lo spazio duale di un prodotto di algebre di Boole e le compattificazioni di Stone

Summary This paper is concerned with the Stone space X of a direct product of infinitely many Boolean algebras. In paragraph 2, after recalling that X is the Stone-ech compactification of the sum (disjoint union) of the Stone spaces of the algebras B_i, we exhibit a compactification of which is not a Stone space and we give a method to construct all the «Stone compactifications» of (the corresponding Boolean algebras are easily characterised). In paragraph 3, a set of ultrafilters of B (the «decomposable» ultrafilters) are introduced: this set properly contains , but, as is shown in paragraph 5, there are direct products that admit nondeeomposable ultrafilters (this is the case iff the set {Card B_i: i I } is not bounded by a natural number). In paragraph 4, among other things, we prove, for the set of decomposable ultrafilters, a weak form of countable compactness, in the sense that every countable clopen cover has a finite subcover; then, we deduce that the set of decomposable ultrafilters is pseudocompact, while obviously is not. Lastly, in paragraph 6, we give a second characterisation of the Stone space of B, showing that every ultrafilter of B can be obtained by iterating in a suitable way the procedure which leads to the construction of decomposable ultrafilters.

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Lavoro eseguito nell'ambito dell'attività del Comitato Nazionale per le Scienze Matematiche del C.N.R.     

Some results on geodesic mappings of Riemannian manifolds satisfying the conditionR.R.=Q(S,R)

In this paper geodesically corresponding metricsg and on a manifoldM, dim 5, under the assumption that the tensorsR andS of the metricg satisfyR.R=Q(S, R), are considered. It is stated that the corresponding tensors and of not necessarily must satisfy . Certain relations between the curvatures ofg and are obtained.Supported by a post-doctoral fellowship of the researchcouncil of the KU Leuven; Bitnet FGBDA3O at BLEKUL11     

A note on threefolds with a hyperplane section of general type

This paper deals with polarized pairs , where is a nonsingular projective threefold and is a very ample line bundle on it, such that for one smooth member  | |, one has (Â)=2. A large class of pairs whose adjoint line bundle is nef and big was indirectedly studied by Beltrametti and co-workers. We add some more information, both in this general case and also when the adjoint line bundle fails to be nef and big.     

Level surfaces of non-degenerate functions inR n+1

We study level surfaces of non-degenerate functions inR ⁿ⁺¹. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field for level surfaces of a non-degenerate function and give certain characterizations of when is transversal, by the shape operatorS, the transversal connection , and consider the difference between and the affine normal.     

Repleteness and regular lattice measures

Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures and on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto , and µ; and try to set some new criterion for repleteness and measure repleteness.     

Notes on Brown-McCoy-radicals for Γ-near-rings

The Brown-McCoy radical is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals, and , respectively, for zerosymmetric -near-rings. Both and are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric -near-ring with left operator near-ringL, it is shown that , with equality ifM has a strong left unity. is extended to the variety of arbitrary near-rings, and and are extended to the variety of arbitrary -near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA N, then , with equality ifA if left invariant.     

A class of extreme contractions inL(l p )

Summary In this note we prove that: if T is a contraction in L(l^p) that maps elements of disjoint support to elements of disjoint support, then T is an extreme point of the unit ball of L(l^p), 1

i) form a p-orthonormal sequence or the nonzero elements of (y_i) form a p-orthonormal sequence for which supp (y_i)=N.     

Sur les idéaux induits dans les algèbres enveloppantes

Résumé Soient une algèbre de Lie de dimension finie et une sousalgèbre de Lie de . Je montre que l'induction, qui envoie les idéaux de l'algèbre enveloppante de dans les idéaux de l'algèbre enveloppante de , commute, à une torsion près, à l'anti-automorphisme principal. La résolution libre standard de la représentation triviale d'une algèbre de Lie joue un rôle important dans la démonstration.

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Summary Let be a finite dimensional Lie algebra, and a Lie subalgebra. I show that the induction map, between the sets of ideals in the enveloping algebras of and , commutes, up to a twisting, with the principal anti-automorphism. The standard free resolution of the trivial representation of a Lie algebra plays an important role in the proof.

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Convention. On fixe un corps commutatifk. Tous les espaces vectoriels, produits tensoriels et algèbres considérés dans cet article sont surk.

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Notations. Si g est une algèbre de Lie, on noteU(g) son algèbre enveloppante. On noteu l'anti-automorphisme principal deU(g): c'est l'antiautomorphisme tel que pourXg. Si est une forme linéaire sur g, nulle sur [g,g], on noteuu l'automorphisme deU(g) tel queX =X+(X) pourXg. Si g est de dimension finie, la fonction module de g est la forme linéaireXtradX.