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Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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 differentiating m-times ( m>-2) the Volterra equation and by integrating the «differential equations system» obtained via the trapezoidal rule. The proposed method has second order and an absolute stability region equal to the third quadrant of the plane ( hλ, h μ). The second part of this paper, analyzes the stability properties and also the order of a class of numerical methods, obtained via the integration of the previous «differential equations system» though backward differentiation. It is shown that these methods have a high order and a very large stability region. [ABSTRACT FROM AUTHOR]

Selection of a technical vocabulary, thesaurus construction and document indexing are critical phases in the organization of Information Retrieval Systems. This paper presents a methodology for the selection of terms to be inserted in a technical vocabulary. After a morphological analysis of texts, a statistical analysis is performed, based on a new method to identify a meaningful interval on the Zipf's frequency distribution of terms. An experiment on a collection consicting of some 5000 abstracts of papers on isotope separation indicates that this method is very promising for automatic selection of technical vocabularies. [ABSTRACT FROM AUTHOR]

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: [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with the language PREFOR, an extention of FORTRAN IV which allows to represent with single identifiers sets of data widely arbitrary and of variable length, The language allows to act upon the sets and upon FORTRAN variables by means of programme defined operators. The declarations of the new operands and operators are added to FORTRAN statements as well as executable statements, describing the calculations upon such elements and FORTRAN expressions, and other organizing statements concerning the dynamic storage assignement required by the variable length operands. Furthermore, referring to the characteristics of dynamic storage organization upon which the language is based, the paper shows the rules for the translation of a PREFOR programme into a FORTRAN programme which can be compiled and executed as usual. Finally a programme is described which can perform this translation upon the IBM 7040 and 7090 and the UNIVAC 1108 processors. [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Some authors have proved that a minimal two-level NAND or NOR network can be obtained by the convetional procedures for determining minimal normal forms. But when either the complements of some input variables are not available or the gates have a limited number of inputs, the two-level synthesis is generally impossible; and no procedure has been described for the minimal sunthesis of networks having more than two levels of gates. In this paper some new procedures are described for the synthesis of NAND or NOR networks having more than two levels of gates. In the first sections the properties are briefly described, by which a NAND or NOR expression is equivalent to a conventional expression containing only the AND and OR operators; also, the problem of determining a minimal two-level NAND or NOR network is summarized. Then the synthesis of three-level NAND or NOR networks is considered, in case that both the true and complemented values of input variables are available, and the gates can have an unlimited number of inputs (condition 1). A new procedure is described which makes it possible to find one of the minimal NAND or NOR networks, having a tree-shaped structure, and which gives also quasi-minimal solutions for the general case in which the output of a gate can be connected to the inputs of more than one gate of the next level. The procedure derives from the methods described in a preceding paper by the present author for determining the minimal «sums of products of sums» of an assigned function; but some properties and the particular definition of cost make it possible to apply a computation technique, which simplifies this problem considerably. Then the synthesis problem is considered when the gates can have an unlimited number of inputs but the complements of some of the input variables are not available (condition 2). In this case the two-level synthesis is generally impossible (a simple necessary and sufficient condition for a two-level solution to exist is proved); on the contrary, a three-level NAND or NOR network always exists, which implements the assigned function. This network can be determined with the procedure which has been described for determining the minimal three-level networks in condition 1, but the new conditions simplify the problem and a remarkable reduction of the computation work is possible. Lastly the following cases are considered: In these cases a two- or a three-level synthesis may be impossible, but one can always verify whether a two- or a three-level network implementing the assigned function exists. However a simple procedure is described, which always makes it possible to find a quasi-minimal solution characterized by more than three levels of gates. [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper contains the doscription of a method of computation of the power spectrum of a stochastic signal that minimizes the error intrinsic with the direct way of computation. The method is a generalization of the mean value rejection and prewhitening techniques. It grounds itself on the adaptive construction of a filter which transforms the true spectrum in a white one by means of the linear filtering of the signal given, whichever the true spectrum may be. The method is suitable of automatic computation in digital form. Various examples of the results obtained by means of a Fortran IV program, also given in the paper, are furnished and discussed. [ABSTRACT FROM AUTHOR]

In a previous paper the numerical solution of a particular boundary-value problem for the «weakly linear» equation was obtained and the convergence of a suitable finite-difference scheme was proved. This paper is concerned with the more general equation where; the solution is obtained using the same finite-difference scheme as in the previous paper, and sufficient condition for its convergence are given for this new case [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm to bound the condition number in spectral norm of a tridiagonal matrix, with nonzero leading principal minors. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalized monospline connected with quasi-Gaussian functionals. We study some properties of this monospline with particular respect to its sign, and we also obtain bounds on the coefficients of the quasi-Gaussian functionals by means of the above defined function. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm to determ an optimal strategy for sistems with linear constrains. Such method is proved to be computationally efficient and to have minimal storage requirements. Contrary to dynamic programming, the state variable does not have to be discretized. The convergence is monotonic and it is realized in no more than (N+1)-steps, where N is the stages number. An example is solved and the results are presented in [6]. [ABSTRACT FROM AUTHOR]

Following a previous paper [1] we estabilish conditions for the bilateral approximation of the solution of ordinary differential equations using A-stable predictor-corrector formulas. An extension to parametric formulas is carried out and numerical examples concerned with stiff equations are presented. [ABSTRACT FROM AUTHOR]

In this paper a method of E. Polak for solving systems of nonlinear equations is generalized and shown to have superlinear convergence under larger assumptions. The result is obtained giving a new criterion for the convergence of the modified secant method. The convergence does not depend upon the goodness of initial approximation of the solution, and is global for a wide class of functions. Numerical results are reported on some known test problems. [ABSTRACT FROM AUTHOR]

In this paper we given an algorithm of low computational complexity which determines the eigenvalues of a symmetric tridiagonal matrix. The algorithm uses the technique of spectrum slicing together with methods for finding the zeros of polynomials. An application of algorithm for computing Gauss quadrature formulas is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to suggest the application of a statistical error estimate in order to avoid the well-known paradox of Richardson extrapolation: if two consecutive approssimations for error estimate are used, then for the error of the best approximation no estimation is possible. This approach is shown to need a first raw evaluation of the error and a Monte Carlo calculation with sufficiently reduced variance. To conclude, a property is proved wich enables to accelerate the reduction of the variance, when the method of extraction of regular part is used. [ABSTRACT FROM AUTHOR]

In this paper it is proved that the linear functionals defined by Gauss-Tchebychef's quadrature formulae with multiple nodes, have remarkable convergence properties. [ABSTRACT FROM AUTHOR]

The partitioning problem is relevant in many fields and in particular it frequently arises in computer system design, in the allocation of computer information to blocks of storage, and in the assignment of tasks in a multicomputer system. In this paper an efficient algorithm for the partitioning of a new class of graphs, called «basic graphs» with size contraints, is introduced. The algorithm finds the optimal solution in a pseudo polynomial time, as a function of the nodes number and of the size constraints. [ABSTRACT FROM AUTHOR]

In information retrieval systems storage occupancy is in general disregarded to take advantage in running time; in an environment in which retrieval time is not a primary requirement (this is the case of Data Base Machines), transposed files become a very interesting structure; in fact they allow a considerable space saving with respect to fast access structures, such as inverted files. But transposed files, in most cases, are not practicable, as theyare to be searched by a sequential scanning. In this paper a structure is defined to implement transposed files, called 2- B tree, which is a sort of two-dimensional B-tree, and avoid sequential scanning; search in a trasposed file stored as a 2- B tree in π memory pages is 0 (π), while insertion and deletion are 0 (log). Moreover, 2- B tree organization can achieve an improvement in storage requirements up to 42% with respect to inverted file organization. [ABSTRACT FROM AUTHOR]

In this paper we describe a method, based on predictor-corrector formulas, for the bilateral approximation of the solution of special initial value problems for ordinary differential equations. For given predictor-corrector formulas, conditions are stated in order to obtain, at any mesh-point, an interval containing the exact solution. The amplitude of the interval gives an error estimate according to the order of the method. Some numerical examples are considered and relevant results are displayed. [ABSTRACT FROM AUTHOR]

In this paper a local method for fitting a surface from scattered data is presented. It is based on two new types of shape functions: the first one is obtained from a local application of weighted average type method, the second one is obtained through L-splines approximation. Theoretical and numerical aspects of this two types of shape functions are analyzed and numerical performances are evaluated. [ABSTRACT FROM AUTHOR]

In this paper we present a multidimensional Monte Carlo automatic integrator; it is based on an adaptive procedure which has been proposed by R. Cranley and T. N. L. Patterson for one dimension. Here we discuss the theoretical aspects of this integrator and give the integrals by which it has been tested with the relevant results. [ABSTRACT FROM AUTHOR]

In this paper, by means of the concept of chaos, we characterise the class of iterating functions in R for which the method of successive approximation converges from any starting point with the exception of a contable set. [ABSTRACT FROM AUTHOR]

In this paper we give some inequalities for the zeros c of the cilinder function J (x)cosα− Y (x)sindα, 0≤α<π, for the zeros c′ of C′( x) and we make an application to negative zeros a , b of Airy functions Ai(x), Bi(x) of first and second kind respectively. We also make a comparison between inequalities related to the first zero j of the Bessel function J (x) of first kind with ν>0 and other known inequalities. Some results are new, other not, but in this case they are derived in a simpler way than usual ones. [ABSTRACT FROM AUTHOR]

In this paper we present a synthesis algorithm for non-recursive digital filters. By the well-known «frequency sampling method», the approximation problem can be related to a convex optimization problem. Finally, we exhibit a synthesis procedure based on the classical simplex algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let Π denote the space of algebraic polynomials of degree n or less. In this paper we establish the inequality $$d_\infty (f,\Pi _n )< \frac{1}{{2^n n!}}\left\| {f^{(n)} } \right\|_\infty$$ for every f C ([−1, 1]) and f absolutely continuous. A way for obtaining similar inequalities for f C ([−1, 1]) and f absolutely continuous is given. [ABSTRACT FROM AUTHOR]

In this paper a class of real-value continuous functions on R (iterating functions) with a finite number of fixed point is defined. The sequence of iterations is proved to converge to a fixed point for any initial value. An application is proposed here to the computation of the real zeros of a polinomial. [ABSTRACT FROM AUTHOR]

In this paper we obtain a new asymptotic formula for the ultraspherical polynomial P (x), as n→∞, with an error term which is O (n ) uniformly in the interval −1+δ≤ x≤1−δ,δ>0. Very accurate approximations for the zeros of P (x) are also derived from the preceding formula. [ABSTRACT FROM AUTHOR]

In this paper we study a bidimensional model which describes the rising of the sea water caused by wind and atmospheric pressure. In the first paragraph we present the physical conditions which justify the construction of the model based on the shallow water theory. In the second paragraph it is demonstrated why the problem related to the mathematical model, using natural boundary conditions, is well posed. Finally in the third paragraph we show some finite difference schemes for the numerical solution figuring out some stability aspects. [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper a method for the numerical evaluation of improper double integrals is given. [ABSTRACT FROM AUTHOR]

In this paper we consider utility functions which depend on two attributes, and analize their characteristics using a model based on bilinear spline functions. Subjective utility values are taken into account and fitted by means of a bilinear spline. In this way we may obtain a piecewise bilinear surface representing utility. This representation provides us a simple method to analize risk aversion and allows to derive inference procedures about the utility function. Numerical illustrations are included. [ABSTRACT FROM AUTHOR]

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)