Navier-Stokes equation with hereditary viscosity

We rigorously study the Navier-Stokes equation with a hereditary viscous term which depends on the past history. Such models arise in the dynamics of non-Newtonian fluids and also as viscoelastic models for the dynamics of turbulence statistics in Newtonian fluids. This problem is mathematically harder than the conventional Navier-Stokes problem due to the lack of certain global estimates. We prove the local solvability theorem using a suitable intermediate m-accretive quantization of the nonlinear term. Finite speed of propagation property of the vorticity field is also proved.     

On a separation criterion for cohomology groups of (q, n - q)-coronae

We give a separation theorem for (q, n - q)-coronas improving a recent result due to Laurent-Thiébaut and Leiterer.     

Matroid designs of prime power index

A class of BIBD's is constructed with parameters generalizing those of the finite projective geometries. These designs are used to construct matroids in which the hyperplanes are equicardinal and the complement of every hyperplane has prime power cardinality. These so-called matroid designs of prime power index “almost” have the property that the flats of any given rank are equicardinal.     

Semilinear integro-differential equations in Hilbert space

Existence, uniqueness and asymptotic behavior of solutions to integro-differential equations involving monotone operators are discussed.     

Structure of sodium glycodeoxycholate micellar aggregates from small-angle X-ray scattering and light-scattering techniques

Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements were accomplished on sodium glycodeoxycholate (NaGDC) aqueous electrolyte solutions as a function of NaGDC and NaCl concentrations with the aim to determine with satisfactory approximation the NaGDC micellar aggregate structure at a gross molecular level, assuming monodispersity. Different conditions of interparticle interactions by varying ionic strength (NaCl concentration from 0 to 0.70 M) and NaGDC concentration (from 0.02 to 0.10 M) were studied. Smeared scattering intensities and electron pair distance distribution functions, radii of gyration, and aggregate heights are in satisfactory agreement with the corresponding functions calculated using a 2(1) helix as model. It is formed by trimers, each one composed by three NaGDC and nine H2O molecules related by a 3-fold rotation axis, and can be described by a hollow cylinder, probably filled by water molecules, characterized by a conventional radius of 23.7 A and a trimer repeat along the helical axis of 3.6 A. The helix is considerably inhomogeneous since the volume of the cylinder occupied by NaGDC molecules is less than one-third of the total. On the other hand, calculations performed with the average radial electronic density of the helix without water molecules or totally filled by water molecules (a NaGDC/H2O molecular ratio of about 1/50) or by using a three-shell average radial electronic density, independently evaluated on absolute scale, do not show significant differences, thus supporting the helical model. The aggregate size increases for all the samples by increasing either the NaCl or NaGDC concentration. The NaGDC low concentration (0.02 M) samples with NaCl within the range 0.30-0.70 M are characterized by short cylindrical aggregates that do not give rise to sensible interference effects. This assertion is supported by the satisfactory fit between the observed apparent mean hydrodynamic radii and the calculated ones by means of the method of Ortega and Garcia de la Torre (J. Chem. Phys. 2003, 119, 9914), valid for rods with a length-to-diameter ratio > or = 0.1 in dilute solution (noninteracting rods). The NaGDC moderate concentration (0.10 M) samples with NaCl within the range 0.20-0.60 M are characterized by cylindrical aggregates that, in the presence of repulsive Coulombic interactions progressively more and more screened, produce interference effects, due to the hard-body repulsion and attractive forces, but the agreement between observed and calculated SAXS data is satisfactory. The results of the low and moderate NaGDC concentration samples seem to indicate that the aggregation number increase, produced by adding 0.10 M NaCl, is constant within an ionic strength range and occurs by the addition of oligomers formed by trimers. The samples with a variable NaGDC concentration (0.02-0.10 M) at a fixed and high NaCl concentration (0.6 M) contain cylindrical aggregates that give rise to an attractive term effect prevailing on the hard-body repulsive one. The same situation seems to occur in the NaGDC moderate concentration samples.     

Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods. The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P_t. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure ν. Moreover, we solve the Kolmogorov equation and prove the so-called "identite du carre du champs". This will be used to study the Sobolev space W^1,2(H,ν) and to obtain information on the domain of the infinitesimal generator of P_t.     

Stable isotope study of precipitation and cave drip water in Florida (USA): implications for speleothem-based paleoclimate studies†

Stable isotopes of hydrogen and oxygen were used to examine how the isotopic signal of meteoric water is modified as it travels through soil and epikarst into two caves in Florida. Surface and cave water samples were collected every week from February 2006 until March 2007. The isotopic composition of precipitation at the investigated sites is highly variable and shows little seasonal control. The δ¹⁸O vs. δ²H plot shows a mixing line having a slope of 5.63, suggesting evaporation effects dominate the isotopic composition of most rainfall events of less than 8 cm/day, as indicated by their low d-excess values. The δ¹⁸O values of the drip water show little variability (<0.6‰), which is loosely tied to local variations in the seasonal amount of precipitation. This is only seen during wintertime at the Florida Caverns site.

The lag time of over two months and the lack of any relationship between rainfall amount and the increase in drip rate indicate a dominance of matrix flow relative to fracture/conduit flow at each site. The long residence time of the vadose seepage waters allows for an effective isotopic homogenisation of individual and seasonal rainfall events. We find no correlation between rainfall and drip water δ¹⁸O at any site. The isotopic composition of drip water in both caves consistently tends to resemble the amount-weighted monthly mean rainfall input. This implies that the δ¹⁸O of speleothems from these two caves in Florida cannot record seasonal cycle in rainfall δ¹⁸O, but are suitable for paleoclimate reconstructions at inter-annual time scales.? Revised version of a paper presented at the 9th, Symposium of the European Society for Isotope Research (ESIR), 23 to 28 June 2007, Cluj-Napoca, Romania.      

Hyperspectral Imaging in the Medical Field: Present and Future

Abstract

Hyperspectral imaging is an optical method that provides a large amount of information about the investigated object. Its medical applications are reviewed in this article, including tumor delimitation and identification, assessing tissue perfusion and its pathological conditions (including some complications like diabetic foot ulceration), making accurate surgical decisions, evaluating the health of dental structures, etc. Many of the articles show very promising results that required brief comments by the authors. It is clear that choosing the appropriate hyperspectral imaging system for each medical field, together with the most reliable hyperspectral image processing methods, are the main goals of future studies, before hyperspectral imaging becomes a widely applicable evaluation method in medicine. The authors try to answer some questions on this topic and set up some directions for future research.