On a theorem by Sohr for the Navier-Stokes equations

In this paper we study some criteria for the full (space-time) regularity of weak solutions to the Navier-Stokes equations. In particular, we generalize some classical and very recent criteria involving the velocity, or its derivatives. More specifically, we show with elementary tools that if a weak solution, or its vorticity, is small in appropriate Marcinkiewicz spaces, then it is regular.     

Microfluidic sensor based on integrated optical hollow waveguides

A simple integrated optical refractometric sensor based on hollow-core antiresonant reflecting optical waveguides is proposed. The sensor uses the antiresonant reflecting guidance mechanism and permits one to measure the refractive index of a liquid filling the core by simply monitoring the transmitted spectrum. The device has been made with standard silicon technology, and the experimental results confirm numerical simulations performed in one- and two-dimensional geometry. The sensor exhibits a linear response over a wide measurement range (1.3330-1.4450) and a resolution of 9 x 10(-4) and requires a small analyte volume.     

Polystyryl-supported TBD as an efficient and reusable catalyst under solvent-free conditions

Polystyryl supported-TBD (PSTBD) is an efficient and reusable heterogeneous basic catalyst under solvent-free conditions for a variety of organic transformations such as 1,2-epoxide ring-opening, aldol-type condensation and Michael addition.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

Preparation of "high specific activity" radiochemical forms of vanadium,manganese and thallium for metallo-toxicological studies

In this paper are presented the production methods for very "high specific activity" radionuclides (HSA-RN) of vanadium, manganese and thallium which have been developed in our laboratories for labelling different chemical forms of these elements present in the echo-systems in ultra-trace amounts, for metallo-toxicological and bio-kinetic studies. Use was made of both cyclotron and thermal nuclear reactor. If the nuclear reaction product has atomic number different from irradiated target, it is possible separating the radioactive nuclide from irradiated target, without addition of isotopic carrier. This kind of radionuclide is named No Carrier Added, NCA, and his specific activity, As is very high and can reach values close to the theoretical Carrier Free one, CF. The experimental determination of specific activity, chemical and radiochemical purities is mandatory for all these kinds of applications.     

Thermogravimetric and kinetic methods to date wood finds. First results

Fresh (larch and fir, in its white and red varieties) and ancient wood samples (dating respectively to the 13th, 15th and 17th centuries) were subjected to thermogravimetric analysis (TG and DTG). The resulting thermogravimetric data were then used to construct archeometric curves for the wood varieties tested. In a preliminary approach, it was attempted to correlate the onset temperature of the thermogravimetric step corresponding to cellulose decomposition with the age (expressed in centuries) of the samples, although the results obtained were anything but brilliant. More encouraging results were obtained by examining the relationship between wood sample age and the value of the (percent cellulose/percent lignin) ratio computed from the thermogravimetric data. Lastly, a procedure for processing data obtained from the TG curves was applied to a kinetic analysis of the processes that take place when wood samples are subjected to a temperature regime with a constant heating rate, obtaining values for the activation energy of the TG step corresponding to the decomposition of cellulose. Also using these data it was attempted to construct archeometric curves, obtaining results that varied quite significantly according to the wood species tested.     

Some noncoercive parabolic equations with lower order terms in divergence form

This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div(uE), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $.AMS Subject Classification: 35K10, 35K15, 35K65.     

Entire solutions of semilinear elliptic equations in and a conjecture of De Giorgi

In 1978 De Giorgi formulated the following conjecture. Let be a solution of in all of such that and 0$"> in . Is it true that all level sets of are hyperplanes, at least if ? Equivalently, does depend only on one variable? When , this conjecture was proved in 1997 by N. Ghoussoub and C. Gui. In the present paper we prove it for . The question, however, remains open for . The results for and 3 apply also to the equation for a large class of nonlinearities .