Giacomo Lorenzoni

Abstract: Are exposed the mathematical bases of a computer program to numerically solve differential analytical models, i.e. systems of partial differential equations. Are described the analytical properties of two well known models to approximate functions of a variable (the interpolating polynomial and the cubic spline) and new upper bounds for the errors of the second are obtained. Are presented essential aspects of a curve in the multidimensional Euclidean space, in order to define the directional derivative of a function and to obtain an upper bound for the absolute maximum value of a derivative definite on a curve. Is shown, for a point where intersect more curves, the expression of a partial derivative as a linear combination of directional derivatives, and of it is deduced the optimum approximation when the values of these are approximate. Is formulated the expression of a generic differential analytical model, highlighting in detail its arguments, identifying the principal impediment to the knowledge of an its exact solution in not knowing its partial derivatives, circumstantiating the context of information contingently available, and showing how it can be calculated an its numerical solution solving an inherent system of not differential equations. Is exposed in detail the algorithm that expresses a derivative of this system as a linear combination of his variables. Finally it is introduced, describing his use characteristics and essential actions, the program PEEI that was realized, on the basis of the previous treatment, to calculate numerical solutions of differential analytical models.

Abstract: Fundamental concepts of probability and statistics are treated, with the aim to circumstantiate and to establish some procedures of numerical elaboration. For this purpose deductive argumentations are used, performed in terms of logic and mathematical analysis. A wide attention to the preliminary description of the logical and mathematical symbolic tools is dedicated. Are extensively shown fundamental properties and definitions, pertaining to the concepts of event and probability. Is reached the probability density of a random variable, by means of the analysis of properties characteristic of statistical sample and universe. Are presented important aspects of the probability density of a set and of a function of random variables. Essential properties are deduced, whom the probability density the expected value and the variance, of the random variables more used. The statistical test and the inherent hypotheses are treated, widely and in details, and lower bounds for the probability of these are reached. The conditions are shown in order to determine lower and upper bounds for the probability that an unknown quantity is found in one given zone of the real axis. Finally the analysis of variance and the regression analysis are treated, with many particulars and in the generally multidimensional aspect.

Abstract: A procedure is exposed in order to determine the solution of a combinatorial problem. The data of the problem are a natural N and a positive real Δ. The solution of the problem are N positive real such that the succession of the 2^N−1 sums, each defined by possessing like addends the elements of one of the as many combinations of the N numbers, it can increasingly be ordered turning out that the 2^N−2 successive increments are all equal to Δ.

Abstract: The site http://www.giacomo.lorenzoni.name/thermalwall/ presents the program ThermalWall 1.0.0.0 and makes available its free download. The program ThermalWall calculates some fundamental dynamic thermal characteristics, for a arbitrary wall composed of multiple homogeneous layers plans whose boundaries are submitted to sinusoidal variations of temperature or heat flow rate. This characteristics variables are: steady state thermal transmittance, time shift of the periodic thermal transmittance, time shift between the maximum temperature outside and inside, decrement factor. The physical quantities treated and their numerical procedures are those defined in the European Standard EN ISO 13786 December 2007 "Thermal performance of building components - Dynamic thermal characteristics - Calculation methods (ISO 13786:2007)".

Abstract: The site http://www.giacomo.lorenzoni.name/sincronia/ presents the program SINCRONIA 1.0.0.0 which can be used for synchronization and backup of files and folders, and makes available its free download.

Abstract: The site http://www.giacomo.lorenzoni.name/peei_3.0.0.0/ presents the program PEEI which calculates a numerical solution of almost all the systems of partial differential equations who have number of equations equal or greater of the number of unknown functions, and makes available its free download and several examples of its application.