Feebly associative P -hypergroupoids

In this paper we study the hyperstructures, saidP-hypergroupoids, (H, P*) in whichH is a set andP* is one of the hyperoperations defined as follows: ∀(x, y) εH ²,xP*y=xyP orxP*y=Pxy whereP is a subset ofH. In particular we give a general formula for to express the simple hyperproducts ofn elements and then we consider some cases in which (H, P*) is feebly associative. We study, in such cases theβ-relations. Work supported by Italian C.N.R. (G.N.S.A.G.A.) and by the Italian M.U.R.S.T. (National interesting Projects of Research).     

Sui gruppi unitari finitari e sulla congettura di dieudonné

In this paper we consider some questions concerning unitary spaces (V, h), even though (V, h) is not finitely generated. Our main result is as follows: letF be an infinite field of characteristic ≠2 andD anm ²-dimensional central division algebra overF with an involutionj≠1. Let Σ_j(D) denote the subgroup of the multiplicative groupD ^* generated by the non zero symmetric elements. If (V, h) is an infinite dimensional regular unitary space of Witt index at least two overD, then the finitary unitary groupFU(h) is a simple group if and only ifD*=Σ_j(D)[D*, D*]. On the other hand, when (V, h) is not regular,FU(h) cannot be simple since it containsFU ₀(h), the subgroup of elements ofFU(h) acting trivially onrad(V, h), as a normal subgroup. In the non regular case we show that under the above assumptions evenFU ₀(h) is not a simple group.     

Distance and fractional isomorphism in Steiner triple systems

In [8], Quattrochi and Rinaldi introduced the idea ofn ^?1-isomorphism between Steiner systems. In this paper we study this concept in the context of Steiner triple systems. The main result is that for any positive integerN, there existsv ₀(N) such that for all admissiblev≥v ₀(N) and for each STS(v) (sayS), there exists an STS(v) (sayS′) such that for somen>N, S is strictlyn ^?1-isomorphic toS′. We also prove that for all admissiblev≥13, there exist two STS(v)s which are strictly 2^?1-isomorphic. Define the distance between two Steiner triple systemsS andS′ of the same order to be the minimum volume of a tradeT which transformsS into a system isomorphic toS′. We determine the distance between any two Steiner triple systems of order 15 and, further, give a complete classification of strictly 2^?1-isomorphic and 3^?1-isomorphic pairs of STS(15)s.     

Operateurs essentiellement reguliers dans les espaces de Banach

Given a closed operatorA acting in a Banach spaceX, we define the regular (respectively the essentialy regular) spectrum σ _r (A) (respectively σ _e,r (A)) ofA. We prove that σ _r (A) and σ _e,r (A) are a closed subsets of the classical spectrum σ(A) ofA. Morever ifA is bounded we prove that σ _r (A) and σ _e,r (A)) satisfies the spectral mapping theorem.     

An algorithm to compute the number of points on elliptic curves ofj-invariant 0 or 1728 over a finite field

We present an algorithm to compute the number ofF _q -rational points on elliptic curves defined over a finite fieldF _q , withj-invariant 0 or 1728. This algorithm takesO(log³ p) bit operations, werep is the characteristic ofF _q .     

Stochastic integration for abstract,two parameter stochastic processes I. Stochastic processes with finite semivariation in banach spaces

In this paper we define the stochastic integral for two parameter processes with values in a Banach spaceE. We use a measure theoretic approach. To each two parameter processX withX _st ∈L _E ^p we associate a measureI _X with values inL _E ^p . IfX isp-summable, i.e. ifI _X can be extended to aσ-additive measure with finite semivariation on theσ-algebra of predictable sets, then the integralε HdI _X can be defined and the stochastic integral is defined by (H·X) _z =ε _[0,z] HdI _X . We prove that the processes with finite variation and the processes with finite semivariation are summable and their stochastic integral can be computed pathwise, as a Stieltjes Integral of a special type.     

Sur Prolungamento Delle Funzioni Della Prima Classe

It is proved that a setH inR ⁿ has Lebesgue null measure if any function which is the restriction toH of a Baire function defined inR ⁿ is the restriction toH of a derivative of an interval function.     

The interior operation in aψ-density topology

We prove that for an arbitrary setA ? ? its interior in aψ-density topology equalsA ∩ φ^β(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS.     

Subvarieties of the matrix variety of second order

LetR _s be the subalgebra ofM ₂(K[t]/(t ^s )) generated bye ₁₁,e ₂₂,te ₁₂ andte ₂₁, whereK is a field of characteristic 0,K[t] is the polynomial algebra in one variablet and (t ^s ) is the principal ideal inK[t], generated byt ^s . The main result of this paper is that we have described theT-idealT(R _s ). Besides the two matrix polynomial identities — the standart identityS ₄ and the identity of Hall, thisT-ideal is generated by one more explicitly given identity. The algebrasR _s are interesting due to the fact that the proper identities of any subvarietyu of the variety ?=varM ₂(K), generated by the matrix algebraM ₂(K) of second order overK, asymptoticaly coincide with the proper identities of someR _s .     

On convergence of sections of sequences in Banach spaces

An elementary proof of the (known) fact that each element of the Banach space? _w ^p (X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element of? _w ^p (X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications to spaces of compact operators on Banach sequence spaces are considered.     

Everywhere Hölder continuity of the spatial gradient of weak solutions to nonlinear parabolic systems

We consider weak solutions to the parabolic system ?u ⁱ?t?D _α A _i ^α (?u)=B _i(?u) in (i=1,...,) (Q=Ω×(0,T), R ⁿ a domain), where the functionsB _i may have a quadratic growth. Under the assumptionsn≤2 and ?u ?L _loc ^4+δ (Q; R ^nN ) (δ>0) we prove that ?u is locally Hölder continuous inQ.     

The picard group of the variety of plane cuspidal cubics of ℙ3

We give a compactification of the varietyU of non-degenerate plane cuspidal cubics of ?³. We construct this compactification by means of the projective bundleX of a suitable vector bundleE. We describe the intersection ring ofX and, as a consequence, we obtain the intersection numbers ofU that satisfy 10 conditions of the following kinds:ρ, that the plane determined by the cuspidal cubic go through a point;c, that the cusp be on a plane;q, that the cuspidal tangent intersect a line;μ, that the cuspidal cubic intersect a line. Moreover, we prove that the Picard group of the varietyU is a product of two infinite cyclic groups generated byρ andc?q.     

Regular threefolds of general type with p g =0 and large bigenus

The known examples of nonsingular complex projective threefolds of general type with geometric genus p _g =0 and irregularities q ₁=q ₂=0 have bigenus P ₂≤6. In the present paper nonsingular threefolds with p _g =q ₁=q ₂=0 and P ₂=7 or P ₂=8 are constructed.     

Sur la Topologiem-Convexe d’une algèbre localementA-convexe

In a locallyA-convex algebra (E, τ) we consider the associatedm-convex topologym(τ). We show that the completion ofE with respect tom(τ) is always a locallyA-convex algebra contained in the complete locally convex space obtained from (E, τ). The topologym(τ) is also used to characterize locally boundedly multiplicatively convex algebras among locallyA-convex ones.     

Wijsman topology on function spaces

LetC(X,Y) be the space of continuous functions from a metric space (X,d) to a metric space (Y, e).C(X, Y) can be thought as subset of the hyperspaceCL(X×Y) of closed and nonempty subsets ofX×Y by identifying each element ofC(X,Y) with its graph. We considerC(X,Y) with the topology inherited from the Wijsman topology induced onCL(X×Y) by the box metric ofd ande. We study the relationships between the Wijsman topology and the compact-open topology onC(X,Y) and also conditions under which the Wijsman topology coincide with the Fell topology. Sufficient conditions under which the compactopen topology onC(X,Y) is weaker than the Wijsman topology are given (IfY is totally bounded, then for every metric spaceX the compactopen topology onC(X,Y) is weaker than the Wijsman topology and the same is true forX locally connected andY rim-totally bounded). We prove that a metric spaceX is boundedly compact iff the Wijsman topology onC(X, ?) is weaker than the compact-open topology. We show that ifX is a σ-compact complete metric space andY a compact metric space, then the Wijsman topology onC(X,Y) is Polish.     

The coefficients of the Laurent series expansions of real analytic functions

Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated.     

Switching Sets Regolari E Cubiche Rigate DiP G(5,q) Piani Di Tralsazione Ad Essi AssociatiG(5,q) Piani Di Tralsazione Ad Essi Associati

In a recent paper, the authors studied some algebraic hypersurfaces of the third order in the projective spacePG(5,q) and they called them ruled cubics, since they possess three systems of planes. Any two of these constitute a regular switching set and furthermore, if Σ is a given regular spread ofPG(5,q), one of the three systems is contained in Σ. The subject of this note is to prove, conversely, that every regular switching set (Φ, Φ′) with Φ ? Σ is a ruled cubic and to construct, for a generic choice of the projective reference system inP G(5,q), the quasifield which coordinatizes the translation plane Π associated with the spread (Σ ? Φ) ∪ Φ′. The planes Π, of orderq ³, are a generalization of the finite Hall planes.     

Derivations in prime rings

LetR be a prime ring andD a nonzero derivation ofR. If one of the four conditions holds inR, thenR is commutative:

1. (i)
   X ²D(X)?D(X)X²∈Z(R), CharR≠2;     
   
   

Calcul Fonctionnel Holomorphe Global Unicité et Invariance Par Les Homomorphismes D’algebres de Banach

LetA be a commutative Banach algebra with unit. Denote byX _A, the global spectrum ofA. There is a holomorphic functional calculusθ _A:O(X _A)→A such thatθ _A(â)=a. In this paper, we show the uniqueness of the global holomorphic functional calculus and we establish its compatibility with Banach algebra morphisms. We also extend this holomorphic functional calculus to the case ofImc algebras.     

Refining Castelnuovo-Halphen bounds

Fix integers r,d,s,π with r≥4, d?s, r?1≤s≤2r?4, and π≥0. Refining classical results for the genus of a projective curve, we exhibit a sharp upper bound for the arithmetic genus p _a (C) of an integral projective curve C?? ^r of degree d, assuming that C is not contained in any surface of degree <s, and not contained in any surface of degree s with sectional genus >π. Next we discuss other types of bound for p _a (C), involving conditions on the entire Hilbert polynomial of the integral surfaces on which C may lie.