Navier–Stokes equations in aperture domains: Global existence with bounded flux and time‐periodic solutions

We consider the Navier–Stokes equations in an aperture domain of the three‐dimensional Euclidean space. We are interested in proving the existence of regular solutions corresponding to small initial data and flux through the aperture. The flux is assumed to be smooth and bounded on (0, +∞). As a consequence, we prove the existence of a time‐periodic solution corresponding to a time‐periodic flux through the aperture. Finally, we compare our solution with a solution belonging to a wider class, showing that, if such a solution does exist, then the two solutions coincide. Copyright © 2007 John Wiley & Sons, Ltd.     

The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer

We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero, to the solution of the Euler equations under the classical zero-flux boundary condition, and same smooth initial data, in any arbitrarily small neighborhood of the initial time. Convergence does not hold with respect to any space-topology which is sufficiently strong as to imply that the solution to the Euler equations inherits the complete slip type boundary condition. In our counter-example Ω is a sphere, and the initial data may be infinitely differentiable. The crucial point here is that the boundary is not flat. In fact (see Beir?o da Veiga et al. in J Math Anal Appl 377:216–227, 2011) if  W = \mathbb R³₊,{\,\Omega = \mathbb R^3_+,} convergence holds in C([0,T]; W^k,p(\mathbb R³₊)){C([0,T]; W^{k,p}(\mathbb R^3_+))}, for arbitrarily large k and p. For this reason, the negative answer given here was not expected.     

Design of a dual aptamer-based recognition strategy for human matrix metalloproteinase 9 protein by piezoelectric biosensors

MMP-9, human matrix metalloproteinase 9, belongs to the family of zinc-dependent peptide-bond hydrolases and is involved in the degradation of the extracellular matrix (ECM). In clinics, it is well known that elevated MMP-9 serum levels are associated with cardiovascular dysfunctions, several aspects of the physiology and pathology of the central nervous system, neuropsychiatric disorders and degenerative diseases related to brain tumors, and excitotoxic/neuroinflammatory processes. Due to the large interest of diagnostics in this protein, efforts to set up sensitive methods to detect MMP-9 for early diagnosis of a number of metabolic alterations are rapidly increasing. In this panorama, biosensors could play a key role; therefore we explored for the first time the development of an aptamer-based piezoelectric biosensor for a sensitive, label free, and real time detection of MMP-9. The detecting strategy involved two different aptamers in a sandwich-like approach able to detect down to 100 pg mL⁻¹ (1.2 pM) of MMP-9 as detection limit in standard solution. As proof of principle, commercial serum was investigated in terms of possible interferents, their identification and role in MMP-9 detection. The estimated detection limit for MMP-9 is about 560 pg mL⁻¹ (6.8 pM) in untreated serum.     

Belgische Methode zur Bestimmung der in Wasser l?slichen Phosphors?ure in den Superphosphaten

Ohne ZusammenfassungIn französischer Sprache eingeschickt. Uebersetzt von der Redaction.     

Navier–Stokes equations: an analysis of a possible gap to achieve the energy equality

The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes equations. arXiv:1904.07641).

     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.