A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Safety settings in equestrian facilities

In recent years an increased attention has been paid to the risks that can emerge within the equestrian environment. In fact, the activities that are carried out every day, whether of working or sport nature, can cause serious traumatic events. The main problems are related to the following risks: biological and physical contact, followed by chemical, electrical, mechanical risks that are common to also a lot of other situations. All these specific risks, of which we talk about in this work, can be contained through proper training and information of workers. The likelihood of accidents can be reduced also applying appropriate behavioural requirements and certain quality and construction parameters used in structures. Inside the equestrian facilities all the main safety systems should be well indicated, also through appropriate signs

Some remarks on PM2.5

Since 1970, the General Physics Department of «Università degli Studi di Torino» has carried out a project research, on inorganic solid particulate matter. The special issue of Annals of Geophysics, published for Professor Giorgio Fiocco’s 70th birthday, gives us the possibility to make some important remarks on this topic, focusing on PM2.5. This has been possible using all the old and new experimental data of the measures made by the authors of this paper since 1970

A circular economy approach for olive oil industry: From olive pomace to microalgal biomass

In this work olive pomace was used to recover high added value compounds and produce biogas by anaerobic digestion. Moreover, in order to satisfy the circular economy concept, the digestate from the latter process was used as medium for the microalga Chlorella vulgaris growth

Intense events of rainfalls in Piemonte

The possibility of studying the precipitations recorded in a large number of meteorological stations in Piemonte led us to analyse what has happened in the last century. A comparison between periods of 10-20 years, using an arbitrary index of rainfall, shows an increase in intense events in the last 20 years though we can observe a general reduction, in absolute value, of the quantity of rain. It is shown that, in the last 30 years, there has been a change in the granulometric distribution of Suspended Particulate Matter (SPM) which, in standard conditions, might become Condensation Nuclei (CN). This might have infl uenced condensation phenomenon, causing a greater frequency of intense events

Optimal quantum tomography for states, measurements, and transformations

We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.Comment: 4 pages, 1 figur

On sequence spaces for Fr\'echet frames

We analyze the construction of a sequence space $\widetilde{\Theta}$, resp. a sequence of sequence spaces, in order to have $\{g_i\}$ as a $\widetilde{\Theta}$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame for a Fr\'echet space $X_F=\cap_{s\in {\mathbb N}_0} X_s$, where $\{X_s\}_{s\in {\mathbb N}_0}$ is a sequence of Banach spaces

A single machine on-time-in-full scheduling problem

A relevant feature in many production contexts is flexibility. This becomes a key issue, for instance, in the case of third-party cosmetics manufacturing [1]. There, the core business is the production of high quality, fully custom orders in limited batches. Competition is pushing companies to aggressive commercial policies, involving tight delivery dates. At the same time, the custom nature of the orders makes it impossible to keep materials in stock; lead times are always uncertain, often making release dates tight as well, and ultimately yielding unexpected peaks of production loads

Inventory rebalancing in bike-sharing systems

We address an optimization problem arising in rebalancing operations of inventory levels in bike-sharing systems. Such systems are public services where bikes are available for shared use on a short term basis. To ensure the availability of bikes in each station and avoid disservices, the bike inventory level of each station must met a forecast value. This is achieved through the use of a fleet of vehicles moving bikes between stations. Our problem can be classified as a Split Pickup and Split Delivery Vehicle Routing Problem. We propose a formulation in which routes are decomposed in smaller structures and we exploit properties on the structure of the optimal solutions, to design an exact algorithm based on branch-and-price