Su una nuova impostazione per l’analisi dei sistemi ereditari

Riassunto L’uso di relazioni ereditarie con memoria infinita comporta la conoscenza della ?storia? di grandezze fisiche nell’intervallo (— ∞,t]. Nel presente lavoro, prendendo in considerazione inizialmente il caso lineare, si reimpostano tali relazioni ereditarie introducendo la nozione di ?stato? del sistema definito in termini di quantità osservabili in un intervallo finito. Nell’ultima parte si dà un’estensione del procedimento a casi non lineari.

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Summary The hereditary relations with infinite memory imply the knowledge of the ?history? of physical quantities in the intervals (— ∞,t]. In this paper a new approach is given for these hereditary relations, in the linear case, by means of the notion of ?state? of the system. The state is introduced in terms of quantities which are defined in finite intervals. In the last part an extention to nonlinear cases is given.

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Lavoro eseguito nell’ambito del Gruppo Nazionale per la Fisica Matematica del C.N.R.     

Base-promoted cyclization of 1-nitrohydrazones bearing a thioether function

Functionalized 1-nitrohydrazones 5 react with sodium hydride in boiling benzene to afford different types of ring-closed products. The formation of the latter can be ascribed to competitive modes of evolution of first-formed nitrile imines.     

The stability of the solutions of a class of integrodifferential systems with infinite delays

Various stability types, analogous to those in the theory of ordinary differential equations, are defined for some classes of integrodifferential systems of equations with infinite delays. Then, on the basis of a variation of constants formula and some results in functional analysis and Laplace transform theory, some necessary conditions and necessary and sufficient conditions are established in order that the trivial solution of a class of systems may be classified as one of the stability types considered in the definitions.     

Disidein,a pentacyclic sesterterpene condensed with an hydroxyhydroquinone moiety,from the sponge Disidea pallescens

A novel pentacyclic saturated sesterpene condensed with hydroxyhydroquinone moiety, which we named disidein (1), has been isolated from the marine sponge Disidea pallescens as disulfate sodium calcium salt. A minor accompaining compound, which seems a likely precursor of disidein, has been identified as 2-pentaprenylbenzoquinone (7).     

Mercury(II) derivatives of azoles

The reaction between mercury(II) chloride and azoles(pyrazole, 3,5-dimethylpyrazole, benzotriazole, 1,2,4-triazole) afforded mainly N-chloro mercury derivatives, although other reactions, such as the well known ring mercuration or the formation of a complex, were observed simultaneously. Therefore, no simple generalization explains the observed reactivity of azoles towards mercury(II) chloride, each reaction investigated being a different case.     

Spherical means and the restriction phenomenon

Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2) set σ_Θ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ², the inequality.

Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $\frac{1}{2}$ ( $\sqrt 2 + 1/\sqrt 2 $ )≈1.06 on classes of instances of high practical relevance.     

On the solutions of the congruence

In this note, we show that if is a positive integer satisfying the congruence , then .

     

Nickel(II)-catalyzed highly enantioselective hydrophosphination of methacrylonitrile

The dicationic Ni(II) complex [Ni(Pigiphos)(THF)](ClO4)2, [1](ClO4)2 ((R)-(S)-Pigiphos = bis-{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}cyclohexylphosphine), catalyzes the addition of bulky aliphatic secondary phosphines to methaacrylonitrile. This hydrophosphination reaction reaches TON = 900 and enantioselectivities up to 94%. A catalytic cycle involving 1,4-conjugate addition of R2PH to methacrylonitrile is supported by the isolation and characterization of a catalytically active N-coordinated, methacrylonitrile Ni complex.