Particular solutions of a class of higher order ordinary differential equations, with non-constant coefficients, are determined by using the properties of the Laguerre exponentials functions introduced by G. Dattoli and P. E. Ricci in [4]. © 2004, Heldermann Verlag. All rights reserved.

We consider a simple example of a partially dissipative hyperbolic system violating the Shizuta-Kawashima condition, ie such that some eigendirections do not exhibit dissipation at all. In the space-time resonances framework introduced by Germain, Masmoudi and Shatah, we prove that, when the source term has a Nonresonant Bilinear Form, as proposed by Pusateri and Shatah CPAM 2013, the formation of singularities is prevented, despite the lack of dissipation. This allows us to show that smooth solutions to this preliminary case-study model exist globally in time.

t. The present work was inspired by the recent developments in laboratory experiments made on chip, where culturing of multiple cell species was possible.

Ever more organizations, both private and public, are placing a greater importance on employee engagement as a means of generating better organizational climate and higher levels of performance. Actually, employee engagement is part of the strategic management of high performance organization, which pay always more attention to human resource initiatives. Moreover, forms of involvement in the decision processes make more motivating and more satisfying the activity for employees, as they create the conditions for greater inspiration and, in turn, contribute to their well-being.

Here we present some studies on the behavior of individuals in a biological networks. The first study is about Physarum polycephalum slime mold and its ability to find the shortest path in a maze. Here we present a PDE chemotaxis model that reproduce its behavior in a network, schematized as a planar graph, (1). In particular, suitable transmission and boundary conditions at each node of the graph are considered to mimic the choice of such an organism to move from an arc to another arc of the network, motivated by the search for food.

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [-1,1] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

WeinvestigatethelinearstabilityofshearsneartheCouetteflowforaclassof2Dincompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows (U (y), 0) and have an exponential density profile. In the case of the Couette flow U(y) = y, we recover the rates predicted by Hartman in 1975, by adopting an explicit point-wise approach in frequency space. As a by-product, this implies optimal decay rates as well as Lyapunov instability in L2 for the vorticity.

A quadrature rule using Appell polynomials and generalizing both the Euler-MacLaurin quadrature formula and a similar quadrature rule, obtained in Bretti et al [15], which makes use of Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the extrema of the considered interval, is derived. An expression of the remainder term and a numerical example are also enclosed.

We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation, and (iii) different pattern formation during spinodal decomposition of binary mixtures.