Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations. Consequently, we provide a complete characterization of the group and phase velocities for these two cases, together with some non-trivial remarks on the nature of wave dispersion in fractional models.Comment: 18 pages, 7 figure

Quality of Life and psychopathology in adults who underwent Hematopoietic Stem Cell Transplantation (HSCT) in childhood: a qualitative and quantitative analysis.

Background: Patients who undergo pediatric Hematopoietic Stem Cell Transplantation (HSCT) may experience long-term psychological sequelae and poor Quality of Life (QoL) in adulthood. This study aimed to investigate subjective illness experience, QoL, and psychopathology in young adults who have survived pediatric HSCT. Method: The study involved patients treated with HSCT in the Hematology-Oncology Department between 1984 and 2007. Psychopathology and QoL were investigated using the SCL-90-R and SF-36. Socio-demographic and medical information was also collected. Finally, participants were asked to write a brief composition about their experiences of illness and care. Qualitative analysis of the texts was performed using T-LAB, an instrument for text analysis that allows the user to highlight the occurrences and co-occurrences of lemma. Quantitative analyses were performed using non-parametric tests (Spearman correlations, Kruskal-Wallis and Mann-Whitney tests). Results: Twenty-one patients (9 males) participated in the study. No significant distress was found on the SCL-90 Global Severity Index, but it was found on specific scales. On the SF-36, lower scores were reported on scales referring to bodily pain, general health, and physical and social functioning. All the measures were significantly (p < 0.05) associated with specific socio-demographic and medical variables (gender, type of pathology, type of HSCT, time elapsed between communication of the need to transplant and effective transplantation, and days of hospitalization). With regard to the narrative analyses, males focused on expressions related to the body and medical therapies, while females focused on people they met during treatment, family members, and donors. Low general health and treatment with autologous HSCT were associated with memories about chemotherapy, radiotherapy, and the body parts involved, while high general health was associated with expressions focused on gratitude (V-Test \ub1 1.96). Conclusion: Pediatric HSCT survivors are more likely to experience psychological distress and low QoL in adulthood compared with the general population. These aspects, along with survivors' subjective illness experience, show differences according to specific medical and socio-demographic variables. Studies are needed in order to improve the care and long-term follow-up of these families

Lebesgue regularity for differential difference equations with fractional damping

We provide necessary and sufficient conditions for the existence and unique-ness of solutions belonging to the vector-valued space of sequences �(Z, X) forequations that can be modeled in the formΔu(n)+Δu(n)=Au(n)+G(u)(n)+ (n), n ∈ Z,,>0,≥0,where X is a Banach space, ∈ �(Z, X), A is a closed linear operatorwith domain D(A) defined on X,andG is a nonlinear function. The oper-ator Δdenotes the fractional difference operator of order >0inthesense of Grünwald-Letnikov. Our class of models includes the discrete timeKlein-Gordon, telegraph, and Basset equations, among other differential differ-ence equations of interest. We prove a simple criterion that shows the existenceof solutions assuming that f is small and that G is a nonlinear term

Fractional diffusions with time-varying coefficients

This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion $B_H(t)$. We obtain solutions of these equations which are probability laws extending that of $B_H(t)$. Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators $L$ and converting their fractional power $L^{\alpha}$ into Erd\'elyi--Kober fractional integrals. We study also probabilistic properties of the r.v.'s whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed r.v.'s

Environmental quality of the operating theatres in Campania: long lasting monitoring results

In this study the microbiological, physical and chemical results of an investigation concerning the environmental conditions of operating theatres in 38 public hospitals of the Campania Government are presented. The analysis of the results has been made by considering specific standards suggested by national and international regulations. The results showed that 84% of the operating theatres presented normal microbiological values, in relation to the total bacterial load, while 16% did not. By considering the microclimatic monitoring 55% of the operating theatres showed normal values while 45% at least a microclimatic index did not. In relation to the concentrations of anaesthetics gases the survey pointed out that the nitrous oxides was within non prescribed environmental limits (50 ppm for N2O); while 15% of the halogenated was not in normal values

The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index 1<α≤2\bf 1<\alpha \leq 2

We study fundamental properties of the fractional, one-dimensional Weyl operator $\hat{\mathcal{P}}^{\alpha}$ densely defined on the Hilbert space $\mathcal{H}=L^2({\mathbb R},dx)$ and determine the asymptotic behaviour of both the free Green's function and its variation with respect to energy for bound states. In the sequel we specify the Birman-Schwinger representation for the Schr\"{o}dinger operator $K_{\alpha}\hat{\mathcal{P}}^{\alpha}-g|\hat{V}|$ and extract the finite-rank portion which is essential for the asymptotic expansion of the ground state. Finally, we determine necessary and sufficient conditions for there to be a bound state for small coupling constant $g$.Comment: 16 pages, 1 figur

Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.Comment: 41 pages, 8 figure

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

Consumer products, such as foods, contain numerous polymeric and particulate additives that play critical roles in maintaining their stability, quality and function. The resulting materials exhibit complex bulk and interfacial rheological responses, and often display a distinctive power-law response under standard rheometric deformations. These power laws are not conveniently described using conventional rheological models, without the introduction of a large number of relaxation modes. We present a constitutive framework using fractional derivatives to model the power-law responses often observed experimentally. We first revisit the concept of quasi-properties and their connection to the fractional Maxwell model (FMM). Using Scott-Blair's original data, we demonstrate the ability of the FMM to capture the power-law response of ‘highly anomalous’ materials. We extend the FMM to describe the viscoelastic interfaces formed by bovine serum albumin and solutions of a common food stabilizer, Acacia gum. Fractional calculus allows us to model and compactly describe the measured frequency response of these interfaces in terms of their quasi-properties. Finally, we demonstrate the predictive ability of the FMM to quantitatively capture the behaviour of complex viscoelastic interfaces by combining the measured quasi-properties with the equation of motion for a complex fluid interface to describe the damped inertio-elastic oscillations that are observed experimentally.United States. National Aeronautics and Space Administration (Microgravity Fluid Sciences (Code UG) for support of this research under grant no. NNX09AV99G

Profile of Trypanosoma cruzi Infection in a Tropical Medicine Reference Center, Northern Italy

Chagas disease (CD) is endemic in Central and South America, Mexico and even in some areas of the United States. However, cases have been increasingly recorded also in non-endemic countries. The estimated number of infected people in Europe is in a wide range of 14000 to 181000 subjects, mostly resident in Spain, Italy and the United Kingdom