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.     

Time-scale and excitation energy partition in sequential binary decays induced by heavy-ion collisions at ≃6 MeV·A

We studied the sequential binary decay of the systems ³²S+⁴⁵Sc, ⁷⁶Ge, ⁸⁹Y, ⁵⁹Co, ⁶³Cu and ¹⁹F+⁶³Cu induced by collisions at ≃6 MeV·A. The two stages of the process have reaction-times compatible with the dynamics of different mechanisms. The study of the excitation energy partition shows that the reaction mechanism of the first step has influence on the de-excitation of the primary fragments producing two decay components which have different time scale. Received: 25 March 1997 / Revised version: 2 December 1997     

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.     

Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

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.     

A high-voltage lithium-ion battery prepared using a Sn-decorated reduced graphene oxide anode and a LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.5</Subscript>O<Subscript>4</Subscript> cathode

This paper describes the preparation and characterization of a high-voltage lithium-ion battery based on Sn-decorated reduced graphene oxide and LiNi_0.5Mn_1.5O₄ as the anode and cathode active materials, respectively. The Sn-decorated reduced graphene oxide is prepared using a microwave-assisted hydrothermal synthesis method followed by reduction at high temperature of a mixture of (C₆H₅)₂SnCl₂ and graphene oxide. The so-obtained anode material is characterized by thermogravimetric analysis, X-ray diffraction, scanning electron microscopy, and electron diffraction spectroscopy. The LiNi_0.5Mn_1.5O₄ is a commercially available product. The two materials are used to prepare composite electrodes, and their electrochemical properties are investigated by galvanostatic charge/discharge cycles at various current densities in lithium cells. The electrodes are then used to assemble a high-voltage lithium-ion cell, and the cell is tested to evaluate its performance as a function of discharge rate and cycle number.