1,721,026 research outputs found
Precorso di matematica. Appunti ed esercizi.
No full textINDICE
1 I numeri reali...1
1.1 Proprietà...1
1.2 Intervalli...5
1.3 Equazioni...6
1.4 Disequazioni...9
1.5 Relazioni e funzioni...13
2 Il Piano cartesiano...19
2.1 Distanza fra punti...22
2.2 Grafici...25
2.3 Alcune tipologie di funzioni...27
2.4 La retta...36
2.4.1 Definizione di limite...45
2.5 I limiti e le loro proprietà...46
2.6 Calcolo differenziale...52
2.6.1 Definizione di derivata...54
2.7 Differenziali...70
2.8 Integrazione...72
2.8.1 Integrale definito...73
2.8.2 Equazioni differenziali...7
Precorso di matematica-II ed.
No full textINDICE
1 I numeri reali...1
1.1 Proprietà...1
1.2 Intervalli...5
1.3 Equazioni...6
1.4 Disequazioni...9
1.5 Relazioni e funzioni...13
2Il Piano cartesiano...19
2.1 Distanza fra punti...22
2.2 Grafici...25
2.3 Alcune tipologie di funzioni...27
2.4 La retta...36
2.4.1 Definizione di limite...45
2.5 I limiti e le loro proprietà...46
2.6 Calcolo differenziale...52
2.6.1 Definizione di derivata...54
2.7 Differenziali...70
2.8 Integrazione...72
2.8.1 Integrale definito...73
2.8.2 Equazioni differenziali...79
3 Alcune cose da sapere...81
3.1 Approssimazioni...81
3.1.1 Quanti decimali dopo la virgola tenere?...84
3.2 Notazione esponenziale...85
3.3 Calcolatrice scientifica...85
3.3.1 Funzione logaritmo...87
3.4 Diagramma di dispersione...88
4 Esercizi...93
4.1 Equazioni...93
4.2 Disequazioni...94
4.3 Il piano cartesiano...97
4.4 Funzioni...98
4.5 Soluzioni degli esercizi proposti...100
4.6 Simboli più utilizzati...10
A new competition model combining the Lotka-Volterra model and the Bass model in pharmacological market competition
No full textThe diffusion of products that compete in the marketplace is a strategic issue for market analysts.
In this paper, we propose a new model for two competing products that is essentially considered an extension of the Lotka-Volterra competition model. This model was first introduced by Guseo (2004) but the application of the model in a real case was missing from that paper. This extension came from the observation that in a standard Bass model, the role of innovators is vital because it incorporates the innovative effect due to external action (a firm communication, advertising) that is proportional to the residual market. Consequently the role is highly relevant in the initial part of diffusion process even if it progressively reduces. Lotka-Volterra models allow for a definition of the residual market of a product category that is more general with respect to alternative approaches. The residual market is not simply defined as the difference between the initial market potential and the sum of all brands adoptions. Conversely, the adoption of competing products contributes to the residual market with different weights. This generates the perception of brands-specific residual markets. Furthermore, the model overtakes the heavy restriction of synchronicity between the two products and provides a simple solution based on the Bass model
A test for the hypothesis of skew-normality in a population.
Full text linkOne of the extension of the normal distribution is the skewnormal distribution, which, through the variations of a shape parameter regulates the skewness of the distribution, allowing a continuous variation from normality to non-normality. This paper introduces a test for the hypothesis of skew-normality in a population and it is based upon the Anderson-Darling goodness-of-fit tes
A test for the hypothesis of skew-normality in a population
No full textOne of the extensions of the normal distribution is the skew-normal distribution, which through the variations of a shape parameter regulates the skewness of the distribution, allowing for a continuous variation from normality to non-normality. This article introduces a test for the hypothesis of skew-normality in a population, and it is based on the Anderson–Darling goodness-of-fit test
A new competition model combining Lotka- Volterra model and the Bass model in pharmacological market competition
Full text linkThe diffusion of products that compete in the marketplace is a strategic issue for market analysts. In this paper, we propose a new competition model for two competing products essentially thought as an extension of a Lotka-Volterra competition model. This model was introduced the first time by Guseo (2004) but in that paper the application of the model in a real case was missing. This extension came from the observation that in a standard Bass model (1969) the role of innovators has a great importance because it incorporates the innovative effect due to external action (firms communication, advertising) that is proportional to residual market and consequently it is of great relevance in the initial part of diffusion process even if it progressively reduces. Lotka-Volterra models allow for a definition of the residual market of a product category which is more general with respect to alternative approaches. The residual market is not simply defined as the difference between the initial market potential and the sum of all brands adoptions. Conversely, competing products adoptions contribute to the residual market with different weights. This generates brand specific perceived residual markets. Furthermore, the model overtakes the heavy restriction of synchronicity between the two products giving a simple solution based on the Bass model
The exponential family generated by the skew-normal distribution.
Full text linkThe aim of this paper is to consider the SN class of distributions as a member of a broader class of distributions, introducing another structural parameter. The starting point is the study of the Normal curves of the r-th order, (Box, 1953), (Turner, 1960), (Vianelli, 1963), considered also in Azzalini (1986). The arrival point showed in this paper is the obtaining of the exponential family generated by the skew-normal distribution, through the method of exponential tilting introduced by Efron (1981). We proved that this family is an example of extended SN distribution as introduced by Azzalini (1985)
Metodi matematici per l'economia
No full textINDICE
1...I numeri reali...1
1.1...Proprietà...1
1.1.1...Proprietà algebriche...1
1.1.2...Proprietà d'ordine...2
1.2...Intervalli...5
1.3...Insiemi Limitati...7
1.4...Punto di Accumulazione...10
1.5...Equazioni...13
1.6...Disequazioni...16
1.6.1...Disequazioni di secondo grado...18
1.6.2...Disequazioni razionali...19
1.6.3...Disequazioni irrazionali...20
1.6.4...Disequazioni con il modulo...23
2...Relazioni e funzioni...27
2.1...Relazione...27
2.2...Le funzioni...30
2.3...Alcune tipologie di funzioni...36
2.3.1...La retta...37
2.3.2...Funzioni polinomiali...44
2.3.3...Funzione parabolica...47
2.3.4...Funzione potenza...48
2.3.5...Funzioni razionali...50
2.3.6...Funzione valore assoluto...52
2.3.7...Funzione segno...52
2.3.8...Funzione esponenziale...53
2.3.9...Funzione logaritmo...54
2.4...Operazioni con le funzioni...59
2.4.1...Prodotto di composizione...60
2.5...Trasformazioni di posizione e scala...63
3...I limiti...67
3.0.1...Definizione di limite...68
3.1...I limiti e le loro proprietà...68
3.1.1...Convergenza e Divergenza...72
3.2...Limiti di funzioni razionali fratte...77
3.3...Limiti di funzioni irrazionali...78
3.5...Infinitesimi e infiniti...83
3.5.1...Principio di sostituzione degli infinitesimi e infiniti...84
3.6...Asintoti...85
3.7...Forme indeterminate: teorema di De L'Hopital...87
3.7.1...Confronto al limite per funzioni esponenziali, logaritmiche e algebriche...89
3.8...Funzioni continue...91
3.9...Discontinuità...97
4...Calcolo differenziale...101
4.0.1...Definizione di derivata...103
4.1 Funzioni crescenti e decrescenti...108
4.2 Teoremi di Rolle, Lagrange e Cauchy...115
4.3 Studio di funzione...121
4.4 Esercizi svolti...134
5 Funzioni di più variabili...143
5.1 Alcune tipologie di funzioni...146
5.1.1 Funzione di tipo polinomiale...147
5.1.2 Funzione razionale...148
5.1.3 Funzioni irrazionali...148
5.2 Derivazione delle funzioni di più variabili...154
5.3 Curve di livello e derivate parziali...155
5.4 Gradiente...156
5.5 Estremanti di una funzione in due variabili...158
5.5.1 E se l'hessiano dovesse ``venire'' nullo?...162
5.5.2 Massimizzazione vincolata...163
5.6 Funzione di Lagrange...167
6 Equazioni differenziali...169
6.0.1 Equazione differenziale omogenea...171
6.0.2 Equazione differenziale non omogenea...176
6.0.3 Equazioni differenziali con condizioni al contorno...182
6.1 Esercizi svolti...185
7 Algebra lineare...189
7.1 Operazioni con le matrici...193
7.1.1 Prodotto per uno scalare......193
7.1.2 Somma di matrici...193
7.1.3 Prodotto di matrici...195
7.2 Spazi vettoriali...198
7.2.1 Il rango di una matrice...199
7.2.2 Determinante...200
7.3 Sistemi di equazioni lineari...208
7.3.1 Teorema di Rouché-Capelli...209
7.4 Sistemi di equazioni lineari omogenei...217
7.5 Esercizi svolti...219
8 Probabilità...233
8.1 Teoria degli insiemi...233
8.2 Il modello di probabilità...239
8.2.1 Probabilità classica...240
8.2.2 Probabilità frequentista...242
8.2.3 Modello astratto di probabilità...243
8.3 Funzione di probabilità...247
8.4 Lo spazio campionario...251
8.4.1 Spazio campionario finito con punti equiprobabili...251
8.4.2 Spazio campionario finito con punti non equiprobabili...261
8.5 Probabilità condizionata e indipendenza...262
8.6 Variabili casuali...268
8.6.1 Funzione di Ripartizione...270
8.7 Alcune variabili casuali discrete...277
8.8 Alcune variabili casuali continue...280
8.8.1 Approssimazioni...284
8.9 Appendice...285
8.10 Esercizi svolti...286
9 Esercizi...301
9.1 Numeri reali e dintorni...301
9.2 Equazioni...303
9.3 Disequazioni...303
9.4 Piano cartesiano...305
9.5 Funzioni...305
9.6 Calcolo differenziale...307
9.7 Funzioni in più variabili...310
9.8 Massimi, minimi, punti di sella di funzioni in più variabili...312
9.9 Estremi vincolati- Moltiplicatori di Lagrange...314
9.10 Equazioni differenziali...315
9.11 Sistemi di equazioni lineari...316
9.12 Calcolo delle probabilità...320
9.13 Variabili casuali...32
The skew-normal distribution
No full textThe book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The first chapter of this book introduces the skew-normal distribution (SN distribution) in the univariate and multivariate case studying in depth their most interesting and relevant features. In the first part of the chapter definition, properties, the moment generating function and the cumulative function give the characterization of the univariate skew-normal distribution and its appealing theoretical features. A wide discussion about inferential problems connected to the methods of estimation of the parameters finishes with the solutions given in literature to face the troubles. The statistical tests developed to assess the hypothesis of skew-normality in literature are discussed at the end of the first part of the chapter.
In the second part of the chapter, the multivariate skew-normal distribution that naturally extends the univariate case is presented starting from its genesis to its immediate and relevant properties as for example cumulative distribution function and moment generating function. It is also emphasized that a number of properties can be extended from the scalar case to the multivariate case. The discussion about the good tractability of linear and quadratic forms highlights as a relevant result the extension of Fisher-Cochran theorem to the SN case. In addition, the conditional distribution associate to a bivariate skew-normal variable is given and it is underlined that conditional mean and variance can be written as a function of the hazard function of the standard normal density. Finally, some results about the SN class in some contexts are analyzed: in particular, the problem of reliability and that of finding regions of assigned probability and minimum volume
Competition Modelling in Multi-Innovation Diffusions: Multivariate Cellular Automata and Differential Approaches
No full textWe introduce a deterministic one–dimensional Cellular Automata model, CA, following Boccara (2004) and extend it to a suitable bivariate probabilistic version where an agent may select, at time t, at most one between two competing innovations. This bivariate automaton is then simplified under a “mean-field approximation”, obtaining a continuous representation that gives rise to the Guseo–Bonaldo synchronic duopolistic model, GB–M (see Bonaldo (1991)). Moreover, we study some characterizations of the more complex two–fold diachronic case
- …
