Inovative management: Basic definitions

First Definitions and Basic Codes

Learnability : Basic Definitions , Examples , Results

The notion of learnability plays a central role in learning theory and continues to be an active topic of study. As noted in the last lecture, it is related to the notion of statistical consistency, with origins in theoretical computer science. Over the next few lectures, we will study various models of learnability related to the probably approximately correct (PAC) learning model introduced i...

Food Security – definitions and drivers 1. Some basic definitions

The concept of food security has been defined on numerous occasions by the international community and it has evolved considerably over time. One of the most fundamental shifts has been the change from an initial concept in which food security was considered equivalent to the reliable availability of food towards the contemporary notion in which food is one of the elements of a complex social c...

Modules I: Basic definitions and constructions

In constrast to group actions, however, one cannot always convert left module structures to right structures and vice versa. To clarify the situation, it is convenient to introduce the opposite ring R, which has the same underlying abelian group R but with multiplication a · b = ba. Then a left module over R is the same thing as a right module over R, and vice versa. Consequently, if R happens ...

I. Groups: Basic Definitions and Examples

Definition 1: An operation on a set G is a function ∗ : G×G→ G. Definition 2: A group is a set G which is equipped with an operation ∗ and a special element e ∈ G, called the identity, such that (i) the associative law holds: for every x, y, z ∈ G, x ∗ (y ∗ z) = (x ∗ y) ∗ z; (ii) e ∗ x = x = x ∗ e for all x ∈ G; (iii) for every x ∈ G, there is x′ ∈ G (so-called, inverse) with x ∗ x′ = e = x′ ∗ ...