Proposta di Dimostrazione della variante Riemann di Lagarias (RH1) equivalente all’Ipotesi di Riemann RH, con RH1 = RH.

Scopo del presente lavoro è quello di proporre una dimostrazione dell'Ipotesi di Riemann attraverso quella che tecnicamente viene definita "variante di Lagarias". Anche se l'obiettivo non fosse stato completamente raggiunto, certamente tale lavoro fornirà un notevole contributo al futuro sviluppo ed alle applicazioni fisico-teoriche dell'Ipotesi di Riemann, che ci inducono a credere alla "realtà" dell'Ipotesi medesima

Teoremi sulle coppie di Goldbach e le coppie di numeri primi gemelli: connessioni tra Funzione zeta di Riemann, Numeri Primi e Teoria di Stringa.

Scopo del presente lavoro è quello di evidenziare le relazioni matematiche tra teoria di stringa e funzione zeta di Riemann, in maniera specifica tra teoria di stringa, Congettura di Goldbach (Teorema di Goldbach) e Teorema di Goldston-Montgomery. Nella prima parte, quindi nel primo capitolo, vengono esposti alcuni teoremi e dimostrazioni matematiche sulle coppie di Goldbach e le coppie di numeri primi gemelli, e delle proposte di soluzione per alcuni problemi additivi di tipo Goldbach e sugli insiemi sparsi ed intervalli corti. Il linguaggio matematico usato in questa parte del lavoro è di tipo puramente algebrico. Nella seconda parte, invece, vengono esposti alcuni settori inerenti la teoria di stringa, precisamente le soluzioni cosmologiche da un sistema D3/D7, la soluzione applicata alla supergravità 10-dimensionale di tipo IIB ed alcune soluzioni solitoniche in teoria di campo di stringa. Verrà quindi evidenziato come queste soluzioni di equazioni di teoria di stringa sono ottimamente correlate con i teoremi di Goldbach e di Goldston-Montgomery e, conseguentemente, con la funzione zeta di Riemann

Organocatalizzatori e liquidi ionici supportati: nuovi materiali in sintesi organica

Nell’ultimo decennio l’organocatalisi e i liquidi ionici hanno rappresentato due campi di grande interesse scientifico. Gli organocatalizzatori hanno trovato particolare impiego in sintesi enantioselettive conducendo a prodotti finali con alte rese e selettività. I liquidi ionici sono stati estensivamente utilizzati come solventi alternativi e, opportunamente modificati, come catalizzatori o loro supporti. Uno sviluppo attuale che accomuna questi due campi di ricerca consiste nella possibilità di immobilizzazione di organocatalizzatori e liquidi ionici per trasformarli in materiali riciclabili con ampie capacità di utilizzo in chimica organica. Negli ultimi anni, il nostro gruppo di ricerca si è occupato di organocatalizzatori e liquidi ionici supportati. E’ stata sviluppata una metodologia sintetica per l’ancoraggio di organocatalizzatori su resine polistireniche attraverso una reazione tiolo-ene, permettendo di ottenere un largo numero di materiali catalitici che sono stati impiegati in reazioni aldoliche, di -selenenilazione e di Michael (Figura 1).1-2 Nel campo dei liquidi ionici supportati (SILP) ci siamo occupati del loro uso nel campo delle reazioni catalizzate da metalli che in organocatalisi. Inoltre, i SILP sono stati efficacemente impiegati in reazioni di apertura di epossidi in CO2 supercritica per fornire carbonati ciclici.3-4 In questo campo abbiamo sviluppato due tipi di materiali, monostrato e multistrato (Figura 2)

A regional GIS-based model for reconstructing natural monthly streamflow series at ungauged sites

Several hydrologic applications require reliable estimates of monthly runoff in river basins to face the widespread lack of data, both in time and in space. The main aim of this work is to propose a regional model for the estimation of monthly natural runoff series at ungauged sites, analyzing its applicability, reliability and limitations. A GIS (Geographic Information System) based model is here developed and applied to the entire region of Sicily (Italy). The core of this tool is a regional model for the estimation of monthly natural runoff series, based on a simple modelling structure, consisting of a regression based rainfall-runoff model with only four parameters. The monthly runoff is obtained as a function of precipitation and mean temperature at the same month and runoff at the previous month. For a given basin, the four model parameters are assessed by specific regional equations as a function of some easily measurable geomorphic and climate basins’ descriptors. The model is calibrated by a “two-step” procedure applied to a number of gauged basins over the region. The first step is aimed at the identification of a set of parameters optimizing model performances at the level of single basin. Such “optimal” parameters sets, derived for each calibration basin, are successively used inside a regional regression analysis, performed at the second step, by which the regional equations for model parameters assessment are defined and calibrated. All the gauged watersheds across the Sicily have been analyzed, selecting 53 basins for model calibration and using other 6 basins exclusively for validation purposes. Model performances, quantitatively evaluated considering different statistical indexes, demonstrate a relevant model ability in capturing the observed hydrological response at both the monthly level and higher time scales (seasonal and annual). One of the key features related to the proposed methodology is its easy transferability to other arid and semiarid Mediterranean areas; thus, the application here shown may be considered as a benchmark for similar studies. The calibrated model is implemented by a GIS software (i.e. Quantum GIS 2.10), automatizing data retrieving and processing procedures and creating a prompt and reliable tool for filling/reconstructing precipitation, temperature or streamflow time series at any gauged or ungauged Sicilian basin. The proposed GIS plug-in can, in fact, be applied at any point of the hydrographical network of the region, assessing the precipitation, temperature and natural streamflow series (at the monthly or higher time scales) for a desired time-window

ECOHYDROLOGY IN MEDITERRANEAN AREAS: A NUMERICAL MODEL TO DESCRIBE GROWING SEASONS OUT OF PHASE WITH PRECIPITATIONS

The probabilistic description of soil moisture dynamics is a relatively new topic in hydrology. The most common ecohydrological models start from a stochastic differential equation describing the soil water balance, where the unknown quantity, the soil moisture, depends both on spaces and time. Most of the solutions existing in literature are obtained in a probabilistic framework and under steady-state condition; even if this last condition allows the analytical handling of the problem, it has considerably simplified the same problem by subtracting generalities from it. The steady-state hypothesis, appears perfectly applicable in arid and semiarid climatic areas like those of African's or middle American's savannas, but it seems to be no more valid in areas with Mediterranean climate, where, notoriously, the wet season foregoes the growing season, recharging water into the soil. This moisture stored at the beginning of the growing season (known as soil moisture initial condition) has a great importance, especially for deep-rooted vegetation, by enabling survival in absence of rainfalls during the growing season and, however, keeping the water stress low during the first period of the same season. The aim of this paper is to analyze the soil moisture dynamics using a simple non-steady numerical ecohydrological model. The numerical model here proposed is able to reproduce soil moisture probability density function, obtained analytically in previous studies for different climates and soils in steady-state conditions; consequently it can be used to compute both the soil moisture time-profile and the vegetation static water stress time-profile in non-steady conditions. Here the differences between the steady-analytical and the non-steady numerical probability density functions are analyzed, showing how the proposed numerical model is able to capture the effects of winter recharge on the soil moisture. The dynamic water stress is also numerically evaluated, implicitly taking into account the soil moisture condition at the beginning of the growing season. It is also shown the role of different annual climatic parameterizations on the soil moisture probability density function and on the vegetation water stress evaluation

ModABa MODEL: ANNUAL FLOW DURATION CURVES ASSESSMENT IN EPHEMERAL BASINS

A representation of the streamflow regime for a river basin is required for a variety of hydrological analyses and engineering applications, from the water resource allocation and utilization to the environmental flow management. The flow duration curve (FDC)represents a comprehensive signature of temporal runoff variability often used to synthesize catchment rainfall-runoff responses. Several models aimed to the theoretical reconstruction of the FDC have been recently developed under different approaches, and a relevant scientific knowledge specific to this topic has been already acquired. In this work, a new model for the probabilistic characterization of the daily streamflows in perennial and ephemeral catchments is introduced. The ModABa model (MODel for Annual flow duration curves assessment in intermittent BAsins) can be thought as a wide mosaic whose tesserae are frameworks, models or conceptual schemes separately developed in different recent studies. Such tesserae are harmoniously placed and interconnected, concurring together towards a unique final aim that is the reproduction of the FDC of daily streamflows in a river basin. Two separated periods within the year are firstly identified: a non-zero period, typically characterized by significant streamflows, and a dry period, that, in the cases of ephemeral basins, is the period typically characterized by absence of streamflow. The proportion of time the river is dry, providing an estimation of the probability of zero flow occurring, is empirically estimated. Then, an analysis concerning the non-zero period is performed, considering the streamflow disaggregated into a slow subsuperficial component and a fast superficial component. A recent analytical model is adopted to derive the non zero FDC relative to the subsuperficial component; this last is considered to be generated by the soil water excess over the field capacity in the permeable portion of the basin. The non zero FDC relative to the fast streamflow component is directly derived from the precipitation duration curve through a simple filter model. The fast component of streamflow is considered to be formed by two contributions that are the entire amount of rainfall falling onto the impervious portion of the basin and the excess of rainfall over a fixed threshold, defining heavy rain events, falling onto the permeable portion. The two obtained FDCs are then overlapped, providing a unique non-zero FDC relative to the total streamflow. Finally, once the probability that the river is dry and the non zero FDC are known, the annual FDC of the daily total streamflow is derived applying the theory of total probability. The model is calibrated on a small catchment with ephemeral streamflows using a long period of daily precipitation, temperature and streamflow measurements, and it is successively validated in the same basin using two different time periods. The high model performances obtained in both the validation periods, demonstrate how the model, once calibrated,is able to accurately reproduce the empirical FDC starting from easily derivable parameters arising from a basic ecohydrological knowledge of the basin and commonly available climatic data such as daily precipitation and temperatures. In this sense, the model reveals itself as a valid tool for streamflow predictions in ungauged basins

Parametric uncertainty or hydrological changes?

The model calibration is the way of hydrologists for searching also a physical interpretation of complex interactions acting within a basin. Actually, it can be frequently noticed how model calibration performed on a given time-window may converge to a point in the parameter space that could be distant from another obtainable calibration of the model in the same basin but considering a different time window. Is that again parametric uncertainty or does the trajectory in the parametric space relate about to a slow hydrological basin change? This paper depicts a possible path for detecting changes’ signatures in a streamflow time series. In particular, the paper seeks to draw a way to discern the random variability over different time-windows of the calibrated model parameters set from that induced by the variation in time of some boundary conditions and external forcings. To this purpose, we will refer to a conceptual lumped model for simulating daily streamflow, the EHSM (EcoHydrological Streamflow Model), and to a hypothetical case study. The selected hydrological model requires a total of seven parameters, some of which can be easily related to land use, while others rely on climate variables. The calibration of the EHSM parameters with regard to different time-windows and the analysis of potential impacts of the anthropic variation in land use and/or climatic variability on the calibrated parameters set, will support our investigation

Evaluating the performances of an ecohydrological model in semi-arid river basins

The EHSM (EcoHydrological Streamflow Model) is a conceptual lumped model aimed to daily streamflow simulation. The model, processing daily rainfall and reference evapotranspiration at the basin scale, reproduces surface and subsurface runoff, soil moisture dynamics and actual evapotranspiration fluxes. The key elements of this numerical model are the soil bucket, where rainfall, evapotranspiration and leakage drive soil moisture dynamics, and two linear reservoirs working in parallel with different characteristic response times. The surface reservoir, able to simulate the fast response of the basin, is fed by rain falling on impervious area and by runoff generated with excess of saturation mechanism while the deep reservoir, which simulates the slow response, is fed by instantaneous leakage pulses coming from the soil bucket. The model has seven parameters, which summarize soil, vegetation and hydrological catchment properties. Parameters can be assessed using simple basic ecohydrological knowledge or Monte Carlo simulations as well. The model has been here calibrated for three semi-arid river basins located in Sicily, Italy with area ranging from 10 up to 1780 Km2 with the aim of investigating how the spatial scale may influence model performances. At the same time, the link between knowledge driven parameters and the calibrated ones is explored, investigating the suitability of a lumped framework for the model as the basin size increases

Generation of natural runoff monthly series at ungauged sites using a regional regressive model

Many hydrologic applications require reliable estimates of runoff in river basins to face the widespread lack of data, both in time and in space. A regional method for the reconstruction of monthly runoff series is here developed and applied to Sicily (Italy). A simple modeling structure is adopted, consisting of a regression-based rainfall-runoff model with four model parameters, calibrated through a two-step procedure. Monthly runoff estimates are based on precipitation, temperature, and exploiting the autocorrelation with runoff at the previous month. Model parameters are assessed by specific regional equations as a function of easily measurable physical and climate basin descriptors. The first calibration step is aimed at the identification of a set of parameters optimizing model performances at the level of single basin. Such "optimal" sets are used at the second step, part of a regional regression analysis, to establish the regional equations for model parameters assessment as a function of basin attributes. All the gauged watersheds across the region have been analyzed, selecting 53 basins for model calibration and using the other six basins exclusively for validation. Performances, quantitatively evaluated by different statistical indexes, demonstrate relevant model ability in reproducing the observed hydrological time-series at both the monthly and coarser time resolutions. The methodology, which is easily transferable to other arid and semi-arid areas, provides a reliable tool for filling/reconstructing runoff time series at any gauged or ungauged basin of a region