In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

Abstract:
We introduce the equation of n-dimensional totally geodesic submanifolds of a manifold E as a submanifold of the second order jet space of n-dimensional submanifolds of E. Next we study the geometry of n-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation of n-dimensional totally geodesic submanifolds. We define the n-Grassmannian structure as the equivalence class of such connections, recovering for n=1 the case of theory of projectively equivalent connections. By introducing the equation of parametrized n-dimensional totally geodesic submanifolds as a submanifold of the second order jet space of the trivial bundle on the space of parameters, we discover a relation of covering between the `parametrized' equation and the `unparametrized' one. After having studied symmetries of these equations, we discuss the case in which the space of parameters is equal to R^n.

Abstract:
Declining energy return on investment (EROI) of a society’s available energy sources can lead to both crisis and opportunity for positive social change. The implications of declining EROI for human wellbeing are complex and open to interpretation. There are many reasons why frugal living and an energy diet could be beneficial. A measure of wellbeing or welfare gained per unit of energy expended (WROEI) is proposed. A threshold is hypothesized for the relation between energy consumption and wellbeing. The paper offers a biophysical-based social science explanation for both the negative and positive possible implications of declining EROI. Two sets of future scenarios based on environmental and economic trends are described. Six types of social change activism are considered essential if the positives of declining EROI are to balance or exceed the negatives.

Abstract:
We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are affine bundles; as a by-product we obtain a new expression for the associated vector bundles. We use Green-Vinogradov formula to provide coordinate expressions for all variational forms, i.e., objects in the finite-order variational sequence on jets of submanifolds. Finally, we formulate the variational problem in the framework of jets of submanifolds by an intrinsic geometric language, and connect it with the variational sequence. Detailed comparison with literature is provided throughout the paper.

Abstract:
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples are provided.

Abstract:
This paper is a natural companion of [Alekseevsky et al.: Contact geometry of multidimensional Monge-Amp\`ere equations: characteristics, intermediate integrals and solutions. Ann. Inst. Fourier (Grenoble) (2012)], generalising its perspectives and results to the context of third-order (2D) Monge-Amp\`ere equations. We use the so-called "meta-symplectic structure" associated with the 8D prolongation $M^{(1)}$ of a 5D contact manifold $M$ and the corresponding notion Lagrangian planes. The analogy with standard symplectic structures allows to write down a geometric definition of a third-order Monge-Amp\`ere equation in terms of a (class of) differential two-form on $M^{(1)}$. In particular, the equations corresponding to decomposable forms admit a simple description in terms of Lagrangian planes which are non-transversal to a certain three-dimensional distribution. We show that such a distribution is made from the characteristics of the original equation, and that there can be up to three mutually orthogonal distributions determining the same equation. We conclude the paper with a study of the intermediate integrals of third-order Monge-Amp\`ere equations of Goursat type.

Abstract:
Humans have been using symbolic representation (i.e. art) as a creative cultural form indisputably for at least 80,000 years. A description of the processes central to the evolution of art from sculpted earthen forms early in human existence to paintings in museums of the modern world is absent in scholarly literature. The present manuscript offers a memetic theory of art evolution demonstrating typological transitions of art in the period post the 3-dimensional to 2-dimensional transition occurring in the early Aurignacian period. The process of art evolution in the 2-dimensional form central to the typological transitions post this period was propelled by material and/or structure chosen to display the artistic message. Symbolic representational tinkering whether collectively or individually creates artistic typologies of display deemed aesthetic and non-aesthetic by the current cultural milieu. Contemporary forms of graffiti underscore the aesthetic/nonaesthetic dichotomy.

This paper will illustrate two versions of an algorithm for finding prime number up to N, which give the first version complexity

(1)

where c1,c2 are constants, and N is the input dimension, and gives a better result for the second version. The method is based on an equation that expresses the behavior of not prime numbers. With this equation it is possible to construct a fast iteration to verify if the not prime number is generated by a prime and with which parameters. The second method differs because it does not pass other times over a number that has been previously evaluated as not prime. This is possible for a recurrence of not prime number that is (mod 3) = 0. The complexity in this case is better than the first. The comparison is made most with Mathematics than by computer calculation as the number N should be very big to appreciate the difference between the two versions. Anyway the second version results better. The algorithms have been

In this paper we will give an algorithm that in the worst case solve the question about the primality of a number in but that gives better result if the number is not prime (constant operation). Firstly, we will introduce an equation on which are based not prime numbers. With this equation it is possible to deduce the prime number that generates a not prime number and to establish an equation in which if exists a certain integer the number is not prime and therefore viceversa to deduce if it is prime.