Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—, we de€ne a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. Œe former is expressed as the di‚erence between changes caused by tim...

The classical Steiner problem is the problem of finding the shortest graph connecting a given finite set of points. In this seminar we review the classical problem and introduce a new, generalized formulation, which extends the original one to infinite sets in metric spaces. Sunto. Il problema classico di Steiner richiede di determinare il grafo di lunghezza minimica che connette un dato insiem...

In the last decades, fractional diierential equations have become more and more popular among scientists and daring engineers in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the au...

One of the most important theorems in Ordinary Di↵erential Equations is Picard’s Existence and Uniqueness Theorem for first-order ordinary di↵erential equations. Why is Picard’s Theorem so important? One reason is it can be generalized to establish existence and uniqueness results for higher-order ordinary di↵erential equations and for systems of di↵erential equations. Another is that it is a g...

In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.

A positive, di eomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure give the two-dimensional axiomatic topological quantum eld theories,...

Let n ≥ 2 be a positive integer and Z× n be the multiplicative group of the integer ring Zn. For a partition {Di|i = 0, 1, · · · , d − 1} of Z× n , if there exist elements g1, · · · , gd of Z× n satisfying Di = giD0 for all i where D0 is a multiplicative subgroup of Z× n , the Di are called generalized cyclotomic classes of order d. There have been lots of studies about cyclotomy with respect t...

This thesis reports on the results of a study of the nested join operator in a mediator-based setting. As the rate at which data is accumulated increases, the need for integration of di erent (physical) Database Management Systems (DBMS) becomes apparent. The most fundamental and arguably important operation that is used in order to achieve this is the join-operator. The nested-relational model...

A short proof of the generalized Faà di Bruno formula is given and an explicit parametrization of the set of indices involved in the coefficient of a specific term of the formula, is provided. An application is also included.

DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P (n)-cohomology of DI(4). We use the non-commutativity of the spectrum P (n) at p = 2 to prove the non-homotopy nilpotency ofDI(4). Concerning the ...