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Aims The aim of this work was to assess the effects of a probiotic diet on well-being of healthy seniors living in boarding and private homes in Marche Region, Italy. In particular, we focused on the modulation of high-sensitivity C-reactive protein (HsCRP), intestinal microbiota and short-chain fatty acids (SCFAs). Methods and Results Ninety-seven healthy seniors took part in a double-blind, placebo-controlled feeding study (59 fed probiotics, 38 fed placebo) for 6 months. Each volunteer ingested daily one food product or a dietary supplement enriched with Synbio® blend (Synbiotec Srl, Camerino, Italy) or the placebo (control group). Blood and faecal samples were collected before and at the end of the intervention period to perform biochemical and microbiological analyses. The serum HsCRP difference value after 6 months of treatment was significantly higher in the probiotic group than placebo (p < 0.05). After the intervention, a significant increase in faecal lactobacilli and a bifidobacteria increase in more participants were observed in the probiotic group. The 16S NGS analysis on the probiotic group showed a decreasing trend of Proteobacteria at the end of the treatment and conversely, an increasing trend of Actinobacteria and Verrucomicrobia phyla, to which the increase of Akkermansiaceae and Bifidobacteriaceae contributes at the family level. Finally, total short-chain fatty acids (SCFAs) and butyric acid were significantly higher in the probiotic group at the end of the treatment respect to the beginning. Conclusions Overall, this study emphasizes the beneficial anti-inflammageing effect of a prolonged diet based on functional foods enriched with Synbio® through the modulation of the intestinal microbiota and the consequent increase in the SCFA production. Significance and Impact of the Study Synbio® integration in elderly daily diet may be a preventive strategy to support healthy ageing.

The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different exchangers, where the heat transfer must be considered within exchangers and outside exchangers. We propose a mathematical model for the study of the heat conduction into the soil as consequence of the presence of exchangers. Such a problem is formulated and solved with an analytical approach. On the basis of such analytical solution, we propose an optimisation procedure to compute the best position of the exchangers by minimising the adverse effects of neighbouring devices. Some numerical experiments are used to show the effectiveness of the proposed method also by taking into account a reference approximation procedure of the problem based on a finite difference method.

New algorithms for the numerical solution of optimization problems involving the $$l_{0}$$ pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral $$\textcircled {1}$$ (grossone) and indicating the number of elements of the set $${\text {I}}\!{\text {N}}$$ , of natural numbers. We show how the numerical system built upon $$\textcircled {1}$$ and the proposed approximation of the $$l_0$$ pseudo-norm in terms of $$\textcircled {1}$$ can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems.

In this study, we propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier–Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger.

We consider an initial–boundary value problem for the two-dimensional Burgers equation on the plane. This problem is reformulated by an equivalent integral equation on the Fourier transform space. For the solution of this integral equation, two numerical methods are proposed. One of these two methods is based on the properties of the Gaussian function, whereas the other one is based on the FFT algorithm. Finally, the Galerkin method with Gaussian basis functions is applied to the original initial–boundary value problem, in order to compare the performances of the proposed methods with a standard numerical procedure. Some numerical examples are given to evaluate the efficiency of the proposed methods. The performances obtained from these numerical experiments promise that these methods can be applied effectively to more complex problems, such as the Navier–Stokes equation and the turbulence flows.

We consider the Volterra integral equation of the first kind for the derivative of a given function with one-side boundary conditions. We give a method to obtain the singular value expansion for the corresponding integral kernel. This singular value expansion can be used to give algorithms for the solution of the numerical differentiation problem. A numerical experiment shows the results obtained by a simple version of such algorithms.

We consider a time-harmonic electromagnetic scattering problem for an inhomogeneous medium. Some symmetry hypotheses on the refractive index of the medium and on the electromagnetic fields allow to reduce this problem to a two-dimensional scattering problem. This boundary value problem is defined on an unbounded domain, so its numerical solution cannot be obtained by a straightforward application of usual methods, such as for example finite difference methods, and finite element methods. A possible way to overcome this difficulty is given by an equivalent integral formulation of this problem, where the scattered field can be computed from the solution of a Fredholm integral equation of second kind. The numerical approximation of this problem usually produces large dense linear systems. We consider usual iterative methods for the solution of such linear systems, and we study some preconditioning techniques to improve the efficiency of these methods. We show some numerical results obtained with two well known Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

An algorithm for the generation of quadrilateral grids on planar domains is presented. This algorithm is given by an iterative procedure, where, starting from an initial grid on the domain under consideration, the coordinates of the grid vertices are iteratively adjusted by using a local discrete variational approach. This procedure resembles the explicit difference scheme for a perturbed heat equation, where the perturbation can be dropped for convex domains. Experimental results on benchmark domains are presented, and show an interesting behavior of the proposed method.

We propose a new direct method to solve linear systems. This method is based on the Sherman–Morrison formula and uses a finite iterative formula. To compare our method with the Restarted Generalized Minimum Residual Method and the Gaussian Elimination Method with Partial Pivoting, we use two classes of test problems: linear systems having Pascal, Cauchy, and Vandermonde matrices as coefficient matrices, and randomly generated linear systems.

We study the existence of special metrics on compact complex manifolds. We show that every considered metric can be caracterized using conditions on the space of positive currents. We investigate what happens under holomorphic submersions or modifications. We show which metrics exist on some classical examples.

We consider the problem of the generation of quadrilateral grids on planar domains. This problem is numerically solved by a two phases method: an iterative procedure based on the well-known variational approach, and an active set procedure to obtain unfolded quadrilaterals. This second phase is performed only when it is really necessary, in fact the first phase alone gives satisfactory results on a large number of domains. This two phases approach provides a robust method with low computational cost. Numerical experiments show that this method is able to generate unfolded grids also on complex domains.

We consider an electromagnetic scattering problem for inhomogeneous media. In particular, we focus on the numerical computation of the electromagnetic scattered wave generated by the interaction of an electromagnetic plane wave and an inhomogeneity in the corresponding propagation medium. This problem is studied in the VV polarization case, where some special symmetry requirements for the incident wave and for the inhomogeneity are assumed. This problem is reformulated as a Fredholm integral equation of second kind, which is discretized by a linear system having a special form. This allows to compute efficiently an approximate solution of the scattering problem by using iterative techniques for linear systems. Some numerical examples are reported.