Long-term Observation of Biochemical Effects of Lead in Human Experiments

Peer Reviewe

Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 86 page

Some sharp inequalities for integral operators with homogeneous kernel

One goal of this paper is to show that a big number of inequalities for functions in L-p(R+), p >= 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp

Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces

We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695]info:eu-repo/semantics/publishedVersio

SARS-CoV-2 variants reveal features critical for replication in primary human cells

Since entering the human population, Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2; the causative agent of Coronavirus Disease 2019 [COVID-19]) has spread worldwide, causing >100 million infections and >2 million deaths. While large-scale sequencing efforts have identified numerous genetic variants in SARS-CoV-2 during its circulation, it remains largely unclear whether many of these changes impact adaptation, replication, or transmission of the virus. Here, we characterized 14 different low-passage replication-competent human SARS-CoV-2 isolates representing all major European clades observed during the first pandemic wave in early 2020. By integrating viral sequencing data from patient material, virus stocks, and passaging experiments, together with kinetic virus replication data from nonhuman Vero-CCL81 cells and primary differentiated human bronchial epithelial cells (BEpCs), we observed several SARS-CoV-2 features that associate with distinct phenotypes. Notably, naturally occurring variants in Orf3a (Q57H) and nsp2 (T85I) were associated with poor replication in Vero-CCL81 cells but not in BEpCs, while SARS-CoV-2 isolates expressing the Spike D614G variant generally exhibited enhanced replication abilities in BEpCs. Strikingly, low-passage Vero-derived stock preparation of 3 SARS-CoV-2 isolates selected for substitutions at positions 5/6 of E and were highly attenuated in BEpCs, revealing a key cell-specific function to this region. Rare isolate-specific deletions were also observed in the Spike furin cleavage site during Vero-CCL81 passage, but these were rapidly selected against in BEpCs, underscoring the importance of this site for SARS-CoV-2 replication in primary human cells. Overall, our study uncovers sequence features in SARS-CoV-2 variants that determine cell-specific replication and highlights the need to monitor SARS-CoV-2 stocks carefully when phenotyping newly emerging variants or potential variants of concern

Toeplitz operators with radial symbols on weighted holomorphic Orlicz space

Peer reviewe

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl