Stepwise retro 1,3-dipolar cycloaddition induced by electron. Impact on 3,5-diphenyl-1,2,4-oxadiazole

The retro 1,3-dipolar cycloaddition induced by electron impact on 3,5-diphenyl-1,2,4-oxadiazole is interpreted as a two-step process on the basis of the energetics and kinetics of the fragments [C₇H₅NO]⁺., [C₆H₅CN]⁺. and [C₆H₅CO]⁺.     

Aging Process Effects on the Characteristics of Vacuum Residue Oxidation Products with the Addition of Crumb Rubber

This paper considers the effect of aging processes on viscoelastic characteristics of vacuum residue oxidation products modified with crumb rubber. Viscoelastic properties were compared to original bitumen raw material-vacuum residue and vacuum residue oxidation products during short-term and long-term aging. The complex shear modulus of the vacuum residue and its oxidation products decreased with an increase in temperature. Short-term aging resulted in increased shear modulus for all samples.The vacuum residue oxidation product modified with crumb rubber had the maximum values of the rutting parameter and fatigue parameter. There was an expansion of the temperature range of plasticity: for the vacuum residue oxidation product with crumb rubber, its value was 67.2 °C. The curves of the black diagram of the modified vacuum residue oxidation product are shifted towards smaller phase angles with the increase in the shear modulus, which indicates the increase in the stiffness and elasticity of the rubber bitumen binders. The vacuum residue oxidation product modified with crumb rubber corresponded to the rubber bitumen binder of the grade RBB 60/90, according to its physical and mechanical indicators.     

Forecasting COVID-19 Epidemic Trends by Combining a Neural Network with Rt Estimation

On 31 December 2019, a cluster of pneumonia cases of unknown etiology was reported in Wuhan (China). The cases were declared to be Coronavirus Disease 2019 (COVID-19) by the World Health Organization (WHO). COVID-19 has been defined as SARS Coronavirus 2 (SARS-CoV-2). Some countries, e.g., Italy, France, and the United Kingdom (UK), have been subjected to frequent restrictions for preventing the spread of infection, contrary to other ones, e.g., the United States of America (USA) and Sweden. The restrictions afflicted the evolution of trends with several perturbations that destabilized its normal evolution. Globally, Rt has been used to estimate time-varying reproduction numbers during epidemics. Methods: This paper presents a solution based on Deep Learning (DL) for the analysis and forecasting of epidemic trends in new positive cases of SARS-CoV-2 (COVID-19). It combined a neural network (NN) and an Rt estimation by adjusting the data produced by the output layer of the NN on the related Rt estimation. Results: Tests were performed on datasets related to the following countries: Italy, the USA, France, the UK, and Sweden. Positive case registration was retrieved between 24 February 2020 and 11 January 2022. Tests performed on the Italian dataset showed that our solution reduced the Mean Absolute Percentage Error (MAPE) by 28.44%, 39.36%, 22.96%, 17.93%, 28.10%, and 24.50% compared to other ones with the same configuration but that were based on the LSTM, GRU, RNN, ARIMA (1,0,3), and ARIMA (7,2,4) models, or an NN without applying the Rt as a corrective index. It also reduced MAPE by 17.93%, the Mean Absolute Error (MAE) by 34.37%, and the Root Mean Square Error (RMSE) by 43.76% compared to the same model without the adjustment performed by the Rt. Furthermore, it allowed an average MAPE reduction of 5.37%, 63.10%, 17.84%, and 14.91% on the datasets related to the USA, France, the UK, and Sweden, respectively.     

Ordinary differential operators in Hilbert spaces and Fredholm pairs

Let be a path of bounded operators on a real Hilbert space, hyperbolic at . We study the Fredholm theory of the operator . We relate the Fredholm property of to the stable and unstable linear spaces of the associated system . Several examples are included to point out the differences with respect to the finite dimensional case, in particular concerning the role of the spectral flow. We define a general class of paths A for which many properties typical of the finite dimensional framework still hold. Our motivation is to develop the linear theory which is necessary for the set-up of Morse homology on Hilbert manifolds. Received: 9 March 2001; in final form: 1 March 2002 / Published online: 2 December 2002     

Characterization of a Marshall-Olkin type class of distributions

Summary A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function. Work performed while the authors were members of CNR-GNAFA.     

Relatively regular ideals in semiprime Banach algebras

Nella prima parte di questo lavoro vengono studiate le relazioni che intercorrono tra il concetto di relativa regolarità in un'algebra non necessariamente unitaria ed alcuni ideali (radicale, zoccolo, prezoccolo) che intervengono nello sviluppo della teoria di Fredholm in algebre di Banach. Nella seconda parte del lavoro viene dimostrato che in certe algebre di BanachA complesse semiprime l'esistenza di un ideale relativamente regolare chiuso implica cheA è unitaria e di dimensione finita.     

Renormalization of non-semisimple gauge models with the background field method

We study the renormalization of non-semisimple gauge models quantized in the 't Hooft-background gauge to all orders. We analyze the normalization conditions for masses and couplings compatible with the Slavnov-Taylor and Ward-Takahashi Identities and with the IR constraints. We take into account both the problem of renormalization of CKM matrix elements and the problem of CP violation and we show that the Background Field Method (BFM) provides proper normalization conditions for fermion, scalar and gauge field mixings. We discuss the hard and the soft anomalies of the Slavnov-Taylor Identities and the conditions under which they are absent.     

Interferometric focal length measurement of power-distributed lenses

An interferometric method for measuring the focal length of power-distributed lenses is described. The test lens is illuminated by a regular pitch interferometric pattern produced by a reflective diffraction grating interferometer. In order to measure the focal length, a CCD camera digitizes the image of the pattern magnified by the lens, and fast Fourier transformed to reconstruct the phase modulo 2π along each row. The change in spatial frequency is determined by unwrapping the phase along each row of the digitized imaged pattern. The technique is used for measuring the focal length distribution inside the progression corridor of both positive and negative progressive lenses.