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In this paper procedures are described allowing the calculation of the cutter position at any given time in two axis, contouring, numerically controlled machinetools. It is assumed that input data define the profile being machined and the cutter offsct and feedrate. The profile consists of straight lines and arcs. It is allowed the cutter offset to be redefined during the machining operation. Procedures mainly consist of a staircase approximation of the theoretical tool-path, as defined from the geometry of the profile and the cutter offset. They require only additions, subtractions and comparisons and are intended for implementation by low-cost special purpose computers.

We propose a numerical method for the approximation of the solution of a variational inequality. The study takes its origin from [1], where a theorem of existence and unicity is proved and from [2], where a procedure is indicated by means of which one can obtain the solution as the common limit of two monotone sequences, the first one being non increasing, the second one non decreasing, whose terms are solutions of elliptic midly non linear problems. In [2] an iterative procedure for the solution of these problems is indicated. The paper aims at describing a numerical procedure for the approximation of the solution. We start by observing that, to obtain a solution within a given approximation, only one of the above mildly non linear problems need be considered, and we construct a convergent difference scheme for the approximation of the solution of such a problem. Finally, an estimate of the error made in this double approximation is given. © 1974 Instituto di Elaborazione della Informazione del CNR.

In this paper we extend the property of a ringA to be of finite real character to loc-etaleA-algebras and to loc-etale neighbourhoods by a suitable representation of these algebras. By this means we get some result on the property to be completely integrally closed for loc-ind-etaleA-algebras and henselizations. We conclude by a counter-example which shows that the properties to be Krull and completely integrally closed are not preserved in the henselization.

In this paper we continue our investigations (see[5]) devoted to transmission problems in consecutive angles, for elliptic operators. In[5] the above mentioned boundary value problems in the case of homogeneous constant coefficient operators and within the Sobolev weight spaces Ws1,s2r were investigated. This work is concerned with the problem for general operators, within the Sobolev weight spaces Ws1,s2r and Ws1,s2*r. Existence theorems and stability theorems for nullity, deficiency, index have been proved.

In this paper the existence of infinitely many eigenvalues for the non linear boundary value problem $$\left\{ \begin{gathered} - \Delta u - \bar \lambda u = \mu \alpha (u) \hfill \\ u|_{\partial \Omega } = 0 \hfill \\ \end{gathered} \right.$$ ΩtRn bounded and\(\bar \lambda \in \) (λ1, λ2)where λ1and λ2are the first and the second eigenvalue of — Δ respectively. The eigenvalues are characterized by the critical levels of a suitable functional on a smooth unbounded manifold. The usual method is not applicable because the functional is not positive definite and the Palais-Smale condition is not satisfied. We applies a technique introduced in a preceding paper [3].

This paper is intended to show that an algebraic approach can give useful suggestions to design efficient algorithms solving combinatorial problems. The problems we discusses in the paper are: a) Counting strings of given length generated by a regular grammar. For this problem, we give an exact algorithm whose complexity is 0 (logn) (with respect to the number of executed operations), and an approximate algorithm which however still has the same order of complexity; b) counting trees recognized by a tree automaton. For this problem, we give an exact algorithm of complexity 0(n) and an approximate one of complexity 0 (logn). For this approximate algorithm the relative error is shown to be 0 (1/n).

This paper deals with the existence of solutions for the implicit Cauchy problem F(t, x, x)=ϑB, x(t0)=x0 in a Banach space B. By using the Kuratowski and the Hausdorff measure of non compactness, we prove an existence theorem for the previous problem (Teorema 1.1) and its extension to non compact intervals (Teorema 2.1). These results generalize the previous ones by R.Conti [1] (in the case B=R), G.Pulvirenti [2] and T. Dominguez Benavides [3], [4] (in the general case). In particular, we relax a Lipschitz condition assumed by all of the abovementioned authors. Some applications of Teorema 2.1 are presented.

In this paper we synthetically proposed the results of the researches made in 18 fields concerning 6 herbaceous cultivations of Sicily (Vicia faba, Tricicum durum cultivar Capeiti, Hedysarum coronairum, Zea mays cultivar " Delkab " and cultivar "Delkab XL 365", Daucus carota) . The data have been taken in several years of observation in the provinces of Caltanis setta, Catania, Enna and Ragusa in order to point out the connections within green area (L.A.I. and G.A.I.), biomass (Kg/ha) and agricultural production (q/ha). From the results obtained we have releved that during the greatest growth of the vegetative apparatus of the plants , the values of L.A.I. are comprised between 1.7 and 4.0 and those ones of G.A.I. between 2.0 and 9.0 in the no well watered fields while in those well watered fields swing between 2.6 and 9.6 the L.A.I. and 5.5 to 11.7 the G.A.I. A very significative datum is the value of L.A.I. (6.9) pointed out in the no well-watered field of Hndyóa/ium coh.ovwU.um of the Plane of Catania. This value is attained in the field of infesting grasses whose G.A.I. is 3.7 superior to that of cultivated species (G.A.I. 3.2). L.A.I. and G.A.I. values have been compared with the biomass and agricultural production. From the data we have point out that the biomass depends from the type and the structure of the cultivation. Its values swing from 1.872 to 7.293 Kg/ha for MixUa aba , from 2.515 to 11.635 Kg /ha for Tricitum durum from 4.705 to 15.304 Kg /ha for Daucus carota, from 4.043 to 8.020 Kg/ha for Hedysarum coronarium. Less variables are the values of the field of Hedysarum coronarium where the biomass swings between 6.915 to 8.752 Kg/ha. We have shewed very high values in the field of Zea mays where the biomass varies from 21.323 to 31.721 Kg/ha. This is due to the altitude, the type of cultivation, the structure of the field. In conclusion we wish to lay stress on the significance of the research made that is very significative for the information in applied field for intervention on the territory., In questo lavoro vengono presentati-sinteticamente i risultati delle ricerche condotte in 18 campi riguardanti 6 colture erbacee della Sicilia (Vicia. faba, Tricitum durum cultivar Capeiti, Hedysarum coronarium, Zea mays, cultivar "Delkab" e cultivar " Delkab XL 365", Daucus carota) . I dati sono stati raccolti, in diversi anni di osservazioni, nei territori delle province di Caltanis setta, Catania, Ernia e Ragusa, al fine di evidenziare le relazioni tra superficie fotosintetizzante (L.A.I. e G.A.I.), biomassa (Kg/ha) e produzione agricola (q/ha). Dai risultati ottenuti si è rilevato che, durante la fase di massimo sviluppo dello apparato vegetativo delle piante, che presentano una notevole variabilità in base al tipo di col¬ tura, i valori del L.A.I. variano da 1,7 a 4,0 e quelli del G.A.I. da 2,0 a 6,0, nelle colture non irrigue, mentre in quelle irrigue i valori sono tutti più elevati oscillando il L.A.I. da 2,6 a 9,6 ed il G.A.I. da 5,5 a 11,7. Un dato significativo , degno di nota ai fini dello studio condotto, è il valore del G.A.I. (6,9) rilevato nel campo di Sulla non irrigato della liana di Catania. Tale valore viene raggiunto per il sopravvento nel campo delle erbe infestanti, il cui G.A.I. è 3,7, superiore quindi a quello della specie coltivata (G.A.I. 3,2). Valori di G.A.I. lievemente diversi sono stati ) rilevati nella stessa coltura in altre condizioni ambientali per diversità di clima, di pratiche colturali, eco. Ciò conferma come anche negli ecosistemi artificiali si possa arrivare ad un massimo di produttività indipendentemente dall'intervento antropico. I valori del L.A.I. e del G.A.I. sono stati inoltre messi in relazione con la biomassa e la produzione agricola. Dai risultati ottenuti si è rilevato che la biomassa dipende dal tipo e dalla struttura della coltura. I suoi valori oscillano nelle varie stazioni da 1.872 a 7.293 Kg/ha per la Fava, da 2.515 a 11.635 Kg/ha per il Grano, da 4.705 a 15.304 Kg/ha per la Carota, da 4.043 a 8.020 Kg /ha per la Sulla. Meno variabili sono i valori per quanto riguarda il campo di Sulla ove la biomassa oscilla tra 6.915 e 8.752 Kg/ha. Valori molto elevati sono stati rilevati per il Mais, la cui biomassa varia da 21.323 a 31.721 Kg /ha. La notevole variabilità riscontrata in funzione dell'altitudine, del tipo di coltura, della struttura del campo, ecc., è stata anche rilevata mettendo in rapporto i valori della biomassa con quelli della superficie fotosintetizzante. Viene, infine, sottolineato il significato dell’indagine condotta che può fornire indicazioni utili in campo applicativo per interventi al territorio., Leonardi Salvatore. Sulla produttivita primaria in colture erbacee della Sicilia. In: Ecologia mediterranea, tome 8 n°4, 1982. pp. 143-164.

The first part of this paper studies the stability and the order of a numerical method for the integration of the second kind of Volterra equations. This method is obtained by differentiatingm-times (m>-2) the Volterra equation and by integrating the «differential equations system» obtained via the trapezoidal rule.

In this paper it is shown that there is no abstract oval of order 10. Also it is shown that there is no partial geometrypg (6,9,4), which in turn would imply the nonexistence of Steiner systemS(3,12,112).

In this paper, for q even, we construct an ovoid O3 and a spread S of the finite classical polar space Q+(7, q) determinated by a hyperbolic quadric Q+ of PG(7, q) such that there is a subgroup of PGO+8(q) isomorphic to PGL2(q3), which maps O3 in itself and S in S and is 3-transitive on O3 and on S; for q>2, S is not a Desarguesian spread of Q+(7, q) and O3 is a Desarguesian ovoid.

An A -semiaffine plane is a linear space with the property that the number π(P,l) of lines through a point P∉l which are parallel to l is a number in the set A . In the paper under review the case A={1,2,3} is completely solved. In fact, the authors show by direct arguments that every finite {1,2,3}-semiaffine plane is naturally embeddable into a finite projective plan

A new representation scheme for solid modelling of polyhedra is discussed, together with algorithms for union, intersection, difference and complementation. The set of models representable in our scheme, containing all the disconnected, nonconvex, unbounded and nonmanifold linear polyhedra, is a Boolean algebra. The range set of the representation scheme is the subset of regular closed 2-complexes, in the sense of algebraic topology. The associated data structure, called winged-triangle representation, uses space 4 E , where E is the number of edges of the triangularized polyhedron boundary. It is space optimal for linearized representations of polyhedra with curved boundary. The algorithms for Boolean operations presented in the paper are very simple and without special cases. The presented approach, based on well-established methods of algebraic topology, can be easily extended to the treatment of objects of dimension higher than three.

In this paper we investigate the boundaries of applicability of the theory of the equilibrium states of Runge-Kutta schemes developed in [1], [2].