A note on weak convergence in L^{1}_{\rm loc}({\mathbb{R}})

Let be a sequence of Borel measurable functions satisfying, for a function the inequalities

Evaporation of a packet of quantized vorticity

We study the diffusion of a packet of quantized vorticity initially confined inside a small region. We find that reconnections fragment the packet into a gas of small vortex loops which fly away. The time scale of the process is in order-of-magnitude agreement with recent experiments performed in 3He-B.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Focal nodular hyperplasia of the liver: diffusion and perfusion MRI characteristics

Purpose

To present diffusion and perfusion magnetic resonance imaging (MRI) characteristics of focal nodular hyperplasia (FNH) of the liver.

Materials and Methods

Thirty-five patients with 52 FNHs (21 were pathologically-confirmed) underwent MRI at 1.5-T device. MR diffusion [diffusion-weighted imaging (DWI)] was performed using a free-breathing single-shot, spin-echo, echo-planar sequence with b gradient factor value of 500 s/mm². MR perfusion [perfusion-weighted imaging (PWI)] consisted of a 3D free-breathing LAVA sequence repeated up to 5 minutes after injection of 7 mL Gd-BOPTA (MultiHance, Bracco, Italy) and 20 mL saline flush at a flow rate of 4 mL/s. Apparent diffusion coefficient (ADC) and time-signal intensity curve (TSIC) were obtained for both normal liver and each FNH by two reviewers in conference; maximum enhancement (ME) percentage, time to peak enhancement (TTP), and maximal slope (MS) were also calculated.

Results

On DWI mean ADC value was 1.624×10^− 3 mm²/s for normal liver and 1.629×10^− 3 mm²/s for FNH. ADC value for each FNH and the normal liver was not statistically different (P= .936). On PWI, TSIC-Type 1 (quick and marked enhancement and quick decay followed by slowly decaying) was observed in all 52 FNHs, and TSIC-Type 2 (fast enhancement followed by slowly decaying plateau) in all normal livers. The mean ME, TTP and MS values were significantly different for FNH and normal liver (P= .005).

Conclusion

FNHs of the liver showed typical diffusion and perfusion MRI characteristics in all cases. On the ADC map, we could get similar value between the FNHs and the background parenchyma. On the perfusion imaging, FNHs showed a different pattern distinguished from the background liver.     

Small values of signed harmonic sums

For every $\tau \in \mathbb{R}$ and every integer N, let ${\mathfrak{m}}_N(\tau )$ be the minimum of the distance of τ from the sums ${\sum }_{n=1}^N{s}_n/n$, where $s_1,\dots ,s_n\in \{?1,+1\}$. We prove that ${\mathfrak{m}}_N(\tau )<\exp ?(?C{(\log ?N)}^2)$, for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than $1/\log ?4$.     

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

This paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.     

Multicategory classification via discrete support vector machines

Discrete support vector machines (DSVM), originally proposed for binary classification problems, have been shown to outperform other competing approaches on well-known benchmark datasets. Here we address their extension to multicategory classification, by developing three different methods. Two of them are based respectively on one-against-all and round-robin classification schemes, in which a number of binary discrimination problems are solved by means of a variant of DSVM. The third method directly addresses the multicategory classification task, by building a decision tree in which an optimal split to separate classes is derived at each node by a new extended formulation of DSVM. Computational tests on publicly available datasets are then conducted to compare the three multicategory classifiers based on DSVM with other methods, indicating that the proposed techniques achieve significantly higher accuracies. This research was partially supported by PRIN grant 2004132117.     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.